Jacob ColvinJacob 222005-11-28T20:05:00Z2006-08-16T20:35:00Z2006-08-16T20:35:00Z1242513826ms115321621911.65680M8R4KGxGuEAAAAAAAAAAAAAAAAAAAAAPgADAP7/CQAGAAAAAAAAAAAAAAABAAAAAQAAAAAAAAAA EAAAAgAAAAEAAAD+////AAAAAAAAAAD///////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////9 ////BgAAAP7///8EAAAABQAAAAcAAAALAAAACAAAAAkAAAAKAAAADAAAAP7////+//////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////1IA bwBvAHQAIABFAG4AdAByAHkAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAWAAUA//////////8EAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACCqpnNzwcYB AwAAAMAPAAAAAAAAXwAxADIAMQA3ADIANAAwADQANQA1AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAABgAAgH///////////////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAA9gEAAAAAAABfADEAMgAxADcAMgA0ADAANAA1ADYAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGAACAAEAAAADAAAA/////wAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAgAAADEAQAAAAAAAF8AMQAyADEANwAyADQAMAA0 ADUANwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAYAAIB//////// ////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAAL8BAAAAAAAAAQAA AAIAAAADAAAABAAAAAUAAAAGAAAABwAAAP7///8JAAAACgAAAAsAAAAMAAAADQAAAA4AAAAPAAAA /v///xEAAAASAAAAEwAAABQAAAAVAAAAFgAAAP7///8YAAAAGQAAABoAAAAbAAAAHAAAAB0AAAAe AAAAHwAAAP7///8hAAAAIgAAACMAAAAkAAAAJQAAACYAAAAnAAAAKAAAACkAAAD+////KwAAACwA AAAtAAAALgAAAC8AAAAwAAAA/v///zIAAAAzAAAANAAAADUAAAA2AAAANwAAAP7///85AAAAOgAA ADsAAAA8AAAAPQAAAD4AAAD+//////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////8ADgAA eJztVk0vA0EYfmam9bEV7EYqEYfGBZE0qIsDFypxQMJBRIT6aFKhVW0l4iKaiF/g5MI/4ObGxRE/ gV/g4qrrne1srR7YRXylz2Z2dt55d553Zp55d29v9Lvj05Z7lGEQAgWzFlUOG1PFQiPAVbtgmqZt Niv4U3ii4lN76Fd14YdjquD7MIkUXVmEEEWS6k1sl6eCNxGEv3TmZT7g19yyXxS7R5y+3Q/Hmczl FRP0vMvtnDKBNax44nRCA2fO+bh9rwk2/xDNfx0bFMciVj3zG8Qvc6Cck1t+6R9Xz0LxjtLqxymS j/BLXp8HfhmrndcLat/sc+9XfdVUaqjUqr4K/idIi7zGs+pewEgdQitqr/zsN9NtLLG0mcqk4tlQ NJ2LZROpZCgS7kYddQ1PlWwIUNtuhCN47D9Lu41AwPeJ+Fsh/2POL+fVj83CSRBH7cHiyIwJTWNG fhl8LwwjH7dq0cAQIOs0oEPj+wMQ9bQQgo4VWafIL4qA7Nb4XgeEbplnaLwAP+iVLxhtr4090rOT 4jicpTJHxA1k1xk/6JNhaMzb+G8OZeSTagLSGXoUaeQQo8yfoOyTpO/AuGptucrKIVo9p57crLnc rx32rptreOX/avxpfkuPUoMkmv0uD1J+V7VOqfWos2JTVfBL8AzICUYEAABVAQAAWgAAAAAMAAB4 nO1Vu04CQRQ9OwM+Fl9sVBJjQaw0JgahstBGMbFQEymMVqKRBKMgLJjYSkL8DT5BOztprIzyCdqb 2NjKeoedxRVRd9UG5Wxm2fuac2fmzqVy678rnY3cowFz4Kga3eiw6RQ5ahgAmJSrhmFYaqONlsIz DY88Q2u08X+whjQ9OQQRRYp+szhubAWfYhje+p0X/YDdsJr+0jQv2n1DjyVdL18pXAjM6imr2Meu K047VDDFvh6ncYOw+Odp/Qc4pDy2seeaXyN+0QPFmpzyC/+E/OaSd4l2P0GZfIdf8Hpc8Itcrb5e ledm3X2vtHVKXRt/G1SLrMt11b1CoSrhqll7jXc/QK/l5E42racTuWA0k4/nkulUMDIVQg+ZFmJ1 HXwkW8JUBE8z5xmnGXB4fpD/KEQruihXpLxVHcL1ZsCcWVG4qipaIQatEAXvV+AjaR3wQ2Un4+B+ 2gCtsCF8a0Z2GjaNRW2siXFaRk6AFWfBe8mB99W8dPJhlo85DfU2MqTeBkPMPYl3UeGPosJmlPlq Yosigzzi1PmT1H1S9D+wIqUjR105SLtnrycney7O68HxCX0Nt/y/jVbmfwFsID7HTgAAAP8DAAD/ AwAA/wMAAP8DAAAAAAAA/wgAAAAAAAAAAAAAAAAAAPQFjwAAAAAAhgEAAE8BAABaAAAAAAwAAHic u3Be8MHCjVIPGdCAHQMzw7//nAxsSGKMUAwGAgwMTFD+v////8OE/4+CIQX+AjELNA5heBSMHBDE kA+EJQwKDK4MeUC6iKESvSjAC8QYWOF5HlQeMJ1jAosfgEi7Ias1eL+wuPjgMUZmINuBEVam+DPk MKSSZCcy4GJgYkT2D7H6RBhg9jsD/Z/LUAB0RxJDFsn2CwHtB3kF5Cdi7QepT4OymaH2egJDPw3o EnLsB9nLQoL9ILfCyvV/0Hgbzf8jEwDTIhMHyakOARiBKYeZC5L20PO+OJDwzUwuyi/OTytRcC0s TSzJzM9TMNYzYOABSrkEw8UYuIF8GEfPmOGL5aZCYl3AzMBCgftlGEDtmJ0HeaH8D1JiDCVnRCEm MzIyc3ExMrXsAOYYVwZmfkYGbkah5nAGBkEGLqYmDQZmQWAACDVHgtSCJZk6jCCSbUJKWCQNoTo1 GZjabBmYgXYyMvOBVRUD1TDB1ECMAZZtQIk8VM0MILO1GTB0GeHSZQTRBSGwyLkyFDKUMiQCS/5M YOmTB6wH/KC8MqJKZQVg6CGnJ2LCHBRfmkTHEGFAqv3UBkPZfgDSZ0jr/wAOAAB4nO1WO28TQRD+ dtdOnMvTFhAJUVipEoGccC6iFEHi4UgUgIQrKuQELBnBGT8SKV1kW1b+hn9CUoWONDRfADEAMgAx ADcAMgA0ADAANAA1ADgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA GAACAQIAAAAGAAAA/////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABcAAAA3 AgAAAAAAAF8AMQAyADEANwAyADQAMAA0ADUAOQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAYAAIB////////////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAIAAAAEkCAAAAAAAAXwAxADIAMQA3ADIANAAwADQANgAwAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABgAAgAFAAAABwAAAP////8AAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAqAAAAvQEAAAAAAABfADEAMgAxADcAMgA0ADAANAA2ADEA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGAACAf////8IAAAA//// /wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADEAAAC/AQAAAAAAAEjAT4BfQEOL j9m9XXPcOeEOEMjInz13u7Mz++1jZuwP79Mfe0eXPyGAGxDou1OY8OmYFoUFgOt+33Vdo3bHGCl8 JUnoO0zqd/8fr2mMv4eHqNKniSwKcOhdx36wFJyLS0gOcl7WA/6OK/1rb3jLb7v2uddonL5hgtoH wtSUB3iOp7E4/bDAmX8/Uf0uwPDfpv2/wEtaxzaexebPEL+sgXI7UfmlfVm3hea9S6dfppX8Cr/k TcTgl2s1db2v783kfVKPTZKkSKYgzxiYJpkhmdW2Y/wfoFjkqdhR9x2MokFYXuwFc3+RHvcqO/Vq o1puZgu13VKzUnWy+dyaCqU7xYFOhZfp5PL4snFci7oCgcRvrP8K5P+YV6frXCseL6Lz9qI3M2PC shKMsUz7CTLtMsQ8wzTjh9eBNCze3SStE9JmllQ75GUP9bIDXrxzIpRNq0RSJ9khaeq+A95ahphT 0zeC1K1ViNkhzGpYfq0fvIi6gBp2UaLKX6Hq49DvwH3d24tUlbN0ev54inLm8r6K/KdmkRGX/09j lPnPixrbRI20WVEGt8hgS4XgGSnRuhYasQcjKrT1TDdVEkhb2StSq6A9DIvnRcGeViaPaB3hTBsy aPhWINNI7cyXL9xM4Fl6KRHIYbnh7lWEvOyzvLyT0o+Rwjd7EFHjAAAAAAAAAAAAAA4AAHic7VbL btNAFD0zk0BxecWqWqliEcGGChSlDiBYtOWVSiygEkVCLMvDahAkpE6Q2CZVld/oH9CuisSCqBJL 4BPgC9iwJebOw2FwA9iAQEE50di+c+71vR6fufG7t7n3m1vTHxDDPAR64QHss+aYGQpHAW7sXhiG 0XQ4wlDhM42MeYdZc+7945pG+Hu4iRr9GsijjCqd1/As3gp+iElk+3te9gP+hqv5V5petH2LHzeD oPuaCbq+yKOesoRHeJAqpw0HnNnPkzRuAlH+K/T8j/GE6riLh6nzu5Rf9kD5TEnzS3/fXAuT9xqt vk+V/Ep+mTeTIr+sNerrPfPeon2fNdx+GmNmfoT/F6RFPpZadV/BSCHC0dqL7/0pOlyv3FurBTW/ kS/XmyuNSq2aLxWKOEjU1eX+HMbJjoxCCZ8ubNeTViCQ+Y36j0F+x7zonjAfNqvdSUwsTek7MyYc J8MY4+svhTjCMM54ZxbIweEbc+CdIi2AzXkWN6u43YFxcc6OKxHntqsYFHcuxn2bT9nE34LbXqXR pBGomfvgrQJZvjrraLd9m6LLqKOJFer8Feo+VfofuGGsp4m6cp5Wz9ZTkjWX72uB/dQtMdLm/9MY 6vyWes4odfDOeaMkvr4jNOvROGtYT3tuPJfRflymrdOQcpNSi4mUGHXD1oyS5CVIIUtfaS3TVbkv zMtkLZqokxA55XKH0sX3hHt8ABnlm4EsXhwiB3FYeQXkw6MbaE9agL27Ta3KKeyJ8r4X5ekofRgq fAFFE2iCAAAAAAAAAAw9nA8MPZgPAAAAAAAAAAAAAAAAAAAAAAAAAAAMPYAPAAAAAAAAAAAAAAAA AAAAAAAMAAB4nLtwXvDBwo1SDxnQgB0DM8O//5wMbEhijFAMBgIMDExQ/r/////DhP+PgiEF/gIx CzQOYXgUjBwQxJAPhCUMCgyuDHlAuoihEr0owAvEGFjheR5UHjCdYwKLH4BIuyGrNXi/sLj44DFG ZiC7gRFWpvgz5DCkkmQnMuBiYGJE9g+x+kQYYPY7A/2fy1AAdEcSQxbJ9gsB7Qd5BeQnYu0HqU+D spmh9noCQz8N6BJy7AfZy0KC/SC3wsr1f9B4g+V9Vih7FIwMAEyLTBwkpzoEYASmFmYuSNpDz/vi QMI3M7kovzg/rUTBtbA0sSQzP0/BWM+AgQco5RIMF2PgBvJhHD1jhi+WmwqJdQEzAwsF7pdhALVj dh40gPJP7BNlKDkjCjGZkZGZi4uRqWUPMzM/IwM3I1OHIQODIAMXU5stA7KoEUgUaA6EAZEGKQVq PYxNK4Ycsj5joJxQcx4DNn1maHKo9oH5QPkQBqHmDCAuBeJisEgKA1OTHpCXBqYhuoWaw4G6XRkK GUoZEoElfyaw9MkD1gN+UF4ZUaWyAjD0kNMTMWEOii8fciILByDVfmqDoWw/AGRoT30ARgAADAAA eJy7cF7wwcKNUg8Z0IAdAzPDv/+cDGxIYoxQDAYCDAxMUP6/////w4T/j4IhBf4CMQs0DmF4FIwc EMSQD4QlDAoMrgx5QLqIoRK9KMALxBhY4XkeVB4wnWMCix+ASLshqzV4v7C4+OAxRmYgu4ERVqb4 M+QwpJJkJzLgYmBiRPYPsfpEGGD2OwP9n8tQAHRHEkMWyfYLAe0HeQXkJ2LtB6lPg7KZofZ6AkM/ DegScuwH2ctCgv0gt8LK9X/QeIPlfVYoexSMDABMi0wcJKc6BGAEphZmLkjaQ8/74kDCNzO5KL84 P61EwbWwNLEkMz9PwVjPgIEHKOUSDBdj4AbyYRw9Y4YvlpsKiXUBMwMLBe6XYQC1Y3YeNIDyT6wX YwiZLQYxmZGRmYuLkallDzMzPyMDNyNThyEDgyADF1NbghKyqBFIFGgOhAGUtmUAKwVqPYyhFZsc sj5joJxQcx4DNn1maHKo9oH5QPkQBqHmDCAuBeJisEgKA1OTHpCXBqYhuoWaw4G6XRkKGUoZEoEl fyaw9MkD1gN+UF4ZUaWyAjD0kNMTMWEOii8fciILByDVfmqDoWw/ABHPT2QAXwAxADIAMQA3ADIA NAAwADQANgAyAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABgAAgD/ //////////////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA4AAAAvwEAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAP///////////////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////////////////AAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///////////////8AAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAAAeJy7cF7wwcKN Ug8Z0IAdAzPDv/+cDGxIYoxQDAYCDAxMUP6/////w4T/j4IhBf4CMQs0DmF4FIwcEMSQD4QlDAoM rgx5QLqIoRK9KMALxBhY4XkeVB4wnWMCix+ASLshqzV4v7C4+OAxRmYgu4ERVqb4M+QwpJJkJzLg YmBiRPYPsfpEGGD2OwP9n8tQAHRHEkMWyfYLAe0HeQXkJ2LtB6lPg7KZofZ6AkM/DegScuwH2ctC gv0gt8LK9X/QeIPlfVYoexSMDABMi0wcJKc6BGAEphZmLkjaQ8/74kDCNzO5KL84P61EwbWwNLEk Mz9PwVjPgIEHKOUSDBdj4AbyYRw9Y4YvlpsKiXUBMwMLBe6XYQC1Y3YeNIDyG2aJMfhIi0FMZmRk 5uJiZGrZw8zMz8jAzcjUYcjAIMjAxdSWoIQsagQSBZoDYQClbRnASoFaD2NoxSaHrM8YKCfUnMeA TZ8ZmhyqfWA+UD6EQag5A4hLgbgYLJLCwNSkB+SlgWmIbqHmcKBuV4ZChlKGRGDJnwksffKA9YAf lFdGVKmsAAw95PRETJiD4suHnMjCAUi1n9pgKNsPAHOnTn8AMABhAG4AZAAlADIAMABTAGUAdAB0 AGkAbgBnAHMAXABKAGEAYwBvAGIAJQAyADAAQwBvAGwAdgBpAG4AXABEAA== Jacob Colvin11/28/2005STAT 6861An Empirical Study of the Behrens DistributionIntroductionDetecting the difference in means for two sample problems is a common question asked by statisticians in practice while in statistics this problem has only been satisfactorily solved in special cases. First, if the two samples are of the same size and can be represented as dependent pairs of observations, the difference between pairs of observations can be considered an independent sample from a t distribution, from which one sample tests can be performed. This is referred to as a paired two sample t test. Alternatively, if the variances for two distinct populations can be shown to have the same variance on theoretical grounds, then a pooled variance 2 sample test can be performed and is distributed according to the well understood t distribution. In practice, many people find the t distribution to be robust enough to provide credible answers as long as the two population sample variances are not significantly different from one another. This assumption is usually checked after the data has been collected to see if thus using a pooled sample variance is acceptable.If two normally distributed populations do not have equal variances, then typically the Welsh approximation has been employed where the pooled sample variance is still used, but the degrees of freedom for the t distribution have been calculated using an elaborate formula.H4sIAAAAAAACC6VVT0gUURj/5nszszuzf31rEKG1CqkRiomnIPCydVqpVgjJYE1XkloNFHTw0qGT p4Tq0CGMukoXC0FD61AghJ3qFBF0r0W7ZLm9PzPTmzVzyFkefL/3/fv93vdm58Pb1w9APvU9EbC4 cSGvcYNsEAAdGoTTYMtCz0JNcy0Nq9WqsDq0w+5ezI+LI6tZT5nVYqbgCFR5MKQZXmPWI7bWMgCf TZbjxsQhPzh5rc+5WQLIYpTt/kCZwR+drXZN1q7HRRiLcSvDrFzc28slvb2GFOe+jcVfX0T2HU4a 2S9dcMpXx28AtCXt5XdfKSw92Zx6yVa28/tUPjmyLvtowPt32SncivDUy85+9TqS9vG966Hg/02p m0jzElccyb2RfIxK7o1k0QrBfaXzH9xlL3R7TetDRmgNLZ2hNUzrG7bU4M0qGpiV5s7KMvoMqc0y 3sSCc2wk79Oe7oW6ELpf7M2P7NI9kAitu3V/3cSv+5BK3bU68wlP5/1MUOc8drtnMI/PM5LPrR34 wwd0xqdvtFyayPaWprIXx8uDYyF1zpn9dbzEKUfiGf2Q4HfCx+fEXWtzvPhZKxh/1g7G90bVeIq3 U6qf4idb9QMpIscdPqaaxFJntvp/OmvPvWLeS6m8J0hF6Oz2eT8NnEPFfCbe3S4/vjkWjN+wVL+t FdOqn+LRQD+KxbiM/8v8au/pak+Fhp7fkOjb7vYZNZpEn5P+vO5GVT/FYwkVA9khHJ/ZxUs70HnP mVtJXmHMP68lwbPfx8sJ/ndfyHnx26aIz3n+VcG738evDDWeYmtS9VM8HwviQlSNB7IgFI34+DRw PJyrvWfagd6nGX1YzP2Sz/t6RMUUf1oqLpLHKLHtfsls8bUT1x0ktzREBFoR30cNsbngTEyWyrDO eQDLaIJZkcADBjYp1M6EiPzfhYkKkrQHAAA= WhereH4sIAAAAAAACC7t+9tgsBjA4wP+AhYETxDIMZQQxmC2ZGBhYGGTAsqxAzMkEYzExMkJZjEz///8H s/QYJaBi3HB1PEwPWA7wCwFZamz8DFIM/0GKGQRAtgFZW4G4gZ+BYSoLUA9UDQ+Db2JJRkhlQSrI cA4g8YsJogMEgAoZdBkhZoswNTFmM4NYwkCWMwtMLJUNJmbLDhFrYLrNBRFrYPLhgYld5IWJefND xBiY73NCxJ4wCXDB7FZAsZsRavcboAqI2gqWcC5Ud1WwxEPlghn2ckHEYCyQWDY/KEx/Myn8h5g8 gRFsPhODQEhmbmqxgl9quUJQfm5iHsOOJZ/LDwKxgsHXcg2+NA2IPUwMILcZcWWwLOMDaTWqhPDd GBeh8IOYelD4GSwruEF8Q7j65dyo6itQ5D8xObKj8hNYIOoh7m/4R577mcFh+QHujwdMx8D2aFbC +HeYQHwNDHsYSQwniD3MUHs4WF7zgkzIg/mH8RuYX1wJk2fjRpX/zYUs/4DJnQ3Ej4TzfZlR+Q4M oKQf7Ioev4wUhY8D8w2wCeGuWMKdCQgFgitzk/JzgHmQj2vnlodCRIbHA6ZlPCAjtF1h/IUcIL4t nG/PCuLrunJBcycXOAeDo5sB4hYBBnYwbw84zzMyMSkFVxaXpOYyaIDsZQDqUGToAmtgBuILj4UY 0P3IDNYPAOEaWIqIBAAA The main advantage with this approach is that while the degrees of freedom will likely not be an integer, through interpolation, t statistics can be approximated with t tables with only integer degrees of freedom.The Behrens distribution (also referred to as the Behrens-Fisher distribution) was introduced in 1929, well before the Welsh approximation which was introduced in 1946. Derived from a Bayesian framework using reference priors, this distribution specifically addressed the general case of two independent normally distributed samples of unequal variances and unequal sample sizes. This distribution is related to the t distribution, but as the convolution of two independent t distributions, and so the exact solution is a rather complicated integral with no real practical way to directly solve for p-values and quartiles.The Behrens distribution (denoted as BF) has 3 parameters; with H4sIAAAAAAACC7t+9tgsBjBwYDzAyMoJYk2JY2QAMpjnAtlMDDJgWVYg5mSCsZgYGaEsRqb///+D WXqMElAxbrg6HqYDjA6MQkCWGhs/gxTDf5BiBgEg/wCQdQzEAxrUBsTcUDU8DL6JJRkhlQWpDAwG YLt/MzX8g7hwAshWJhYmBoHgytyk/BwGBl9hrt4FH4UYdiz5XH4QiBUMvpZ7CKe5sQBV6wIVcwBp I64ERjGQNQyFlVxQW7jALmEEmwqxQ4CBHczbA3Y7IxOTUnBlcUlqLgMDyDwGoA5Fhi6wBpDOPZ+F GCB2MILpD0AZZrB+ACU4jXtQAQAA representing a measure of the ratio of the standard errors of each sample.H4sIAAAAAAACC6VVXUhTURw/59zrvbs7091NiwgflliYqalIipGsqIEPhaQPBQVO3UzIaZtgMx8k RlAPtUgy7AMJH0sQIiR8MIyIUaIo+VYiUvRmSj0UtO75WvcMgz42Lvx/H+d3zvmfs93lNy9HAf2s mP58YJBq8iwkhaKoAKigkKo51mMgUSEIeQVROp2mVQXcwTmc8bmQP3/F9FrVHs0NdoI0MQPTwjNW 9dB6xiywahkw97jA8WDfuZZ4bwiAMdVhsd8QG0E+1oJAOWTZBahBO2CQKh8VaZ2G8PokL+TeUsvB vPPahCHnzGtPubahFjgZJyrCaS7GPXKI+ZKOTkPOv+MQ+Q1Gdn6DIfJbdZEvKsJV8vxC/a3GuEK9 iXML7g2FcQvulCq4VU1wz3TGLZtPMOOWzUCu4F7nCS5sMq7FM8XnrfN8csp78FsM0xa9lVjew6K3 juffy7uNGScqwl0xyT35jnxp1v0kpGeAgNnS1R2K+U6E+n0ne7qDETA1vtn/3Hp8lV/6d+NwPZsH AXJ+1c5Z76SbDK2OM3zD/VjCd80RCc96b7oIrsr4Gf7lb5P0Rs9H3a43et6pdn0YxzS7PoxVSa8w LmG7XmHcl/JmtDZs989oE7odl6q3VLu/VL0K7XgNNknzrcFeyDDr79CPf+uvQn8P65k+13quO0jE 3rjAbQrBJRzX4EFJr8EFdB9lGTysyvgoso8f1Fnfxfg5xwDN289xqyYw5v5xpFtVMNreF4yUqMyV Ui7S06iKMpyAxRxndwP+5W1j3VB4N9q9H/JIQoTPc9BcpzgWFfp7LOtL2K7Xel7QdZ3O4CVFxn5A /hSbjxkUD+SeAopVHY509In+FecQR0dY4Dkk4wBNOBIQ/Sxz2vU5x1e6glhY9FfWWzWfbtdTyiu6 wkgG1wO7PwEfSHoCCj37dw7/6x6OeBBi+9rifiPrazbHu9t6zgPQ5XIm/Z+9f3iitZ6xXBKxLyBw 1CD4UAZP5xBcHhD3NQrtekq5LOkpJYnsegJWSHoChrm+xc1Eqm0feJtz9Pf7yO5PDR6i53Yhs87t gGEnf2M66VuV/h0ANrcJdIqm6XsYIlTUHI/1hbpBPZkHWCN2gWt0ADGc2fSC7B4qdPxPBEr1ZxwI AAA= In 1965, Patil gave an approximation that relates the Behrens distribution to the t distribution (of course in a different way then Welsh). Using this approximation, R source code from “Bayesian Statistics: An Introduction, Third Edition” by Peter M. Lee(2004) was utilized for their implementation of functions such as pbehrens() and hbehrens() which where used in this simulation study. [hbehrens() accepts a p-value and returns a vector of two test statistics representing a two sided “high density region”, which could have been implemented using +/- qbehrens() at half the alpha value.]A Comparison of the DistributionsThe following side by side examples of the Welsh approximation and the Behrens distribution via the Patil approximation where calculated using these values.H4sIAAAAAAACC6WUQWgTQRSG38xu0s1mbbNJ0FIipC1UUAzttEoJCO1BpJAq2IDnlqau4LbqtoTQ S885iBcvFSQHTyKhJ+lBpF6CCJ57XTx7qERPguvM25llN7YXmzDs+/a9N/Pev485/trbB/z5hl+A jLDs20QYWpsCUCihN8VXhiqLEiItQoMgQKtCRuW7bBRnUb/gG3luTaVHYAwCEQw5zkfc+shXxwB4 XeA5MsaC5dVtp9560gA40MXZv+nen7DCF+JQyv+5lZa7tvUY4HnRfNX5kYfDN/3mJ77K07+aX4ob kzoPvM6j+ebAzJcFMy1SD1qKn2H9tyTX7Kt6nHuWReO8Z35LxFeNOwn/z9TlBHe1xQQ75JLkU/oB nfdTf+Q2vPLdRrN8f8td3TyjHwLieRLrq60Lqdmc4rCPSsRvKfpvqD5HhwTPM8WHqEsl4vmU8M/M KV6j8f1qdp7EuWeNaRjPlE5FTfhvMqWThzzLlE7XkFV8V7uXYIcsIU+zUKdy8H86gdSJSJ2mLqSw bibP8c3vED9331hI+OvpKyTuH9arCf9nMi79g9+Tv6V6bD53s+bDs+fz3+95Eet6GulXQvYi/ZLc 1RaQ3Ug/xYP6kXPp985+j3Pw4LR+zzG/NbuLO2xE81fF+tdZBtkamcCMurPjqYkLIzYdNXGKTXl/ mHjH4MBAWG0OhpA+4K1EKJ1YaXnbDRcmRWXAM8ahHSaIqH4eBlXQ0PMXF5dJ+ioFAAA= H4sIAAAAAAACC+3dB3gVRdcH8N3QQhFDFUQFQguC1AChBbBR1ShiQaV3AgQCIUCA0HsM1dBDDxB6 CSUgIFVEQEGQJgoKFqQqiijvTPZePflns+ceHt7vwzfJ8yx3fknITXbnTjln7o5pGEakOkqpw0cd UV6G0V8d7o9PXjKMceoo8sJLLxqGacTeNIx8OQ0jg/paNnUEu78xk2HsUJ/sZaqvm0ayj6BFmQzv GhmN+kYvo7URYnQy6ql/Q5K+VkIdOdThrX4NdzkTKePnX1OPIab+TQzj2r179+jzRFvPa2ZR/9RT z9VZPVuwcb8ffkn/1spf1D+f+smv5jJPhlz3Naqdrd1Xl/UpitlaIul73lCfI6fMKLHeMO5e9TX6 NzjRPEodtXKdaq7Pl/cNX+N2ixPNfa75Jn1fRLMTzW+5/pZcriO3OgomfTX535ZoPYH5rvq/NYrf 6Dtrf7mkc1egq1/SldOPIeprW4vd6Jsj6VuL+hc0VpvR6nMvq8/pv8N9XvMlnSkz6f+tV1+vd+l6 X/ffqb/eXB3twvSp/+f6mKT8iMP1ud/v9/TzjdVjXXVUsGwUcT2X6aq/DV3HBHW+3vBK6dR+bg1X WdfpluoIUIeX69Egj/qZ3NX7HtQY98/T/y/vP3+7UdN6PqOQ63fUP7+e+qaqHroV49ZCt2HcVuh2 Qrdn3EHojow7Cd1Z6C6MuwodLHQ3xt2F7sE4ROieQvdiHCp0b8Z9hA4Tui/jcKH7Cd2f8QChIxgP FHqQ0IMZRwo9hPFQoYcJPZzxCKFHMh4l9GihxzAeK/Q4occzniB0FOP3hY4WeiLjSUJPZjxF6KlC T2P8gdAxQk9nPEPomYxnCT1b6DmM5wody3ie0POFXsB4odCLhF7MeInQcYyXCr1M6OWM44VewXil 0KuEXs14jdBrhV7HeL3QGxhvFDpB6E2MNwu9hfFWoROF3sZ4u9AfMt4h9E6hdzH+SOjdQu9hvFfo fTqG4+D9Qh8Q+mPGB4X+hPEhoT8V+jDjI0IfFfozxp8LfYzxcaG/UEcdgU8wPin0l4xPCX1a6DOM zwp9Th2BAn/F+LzQXzP+RugLHrg28UXG3wr9HeNLQl/WeQuBv2f8g9A/2rimg39ifEXon21cg/iq 0NeEvq6O6g6+IfRNGwcQ3xL6FxtXc/CvjG/buKqDf2P8u42rOPiOB/Yn/oPxXXVUFvhPG1dy8F82 rkh8zwNXINYJKSebyuUF9lIuJ3AG5WccnFG5rMCZlMs4OLPy04xLE2fxwH7E3jYuRZzVxiUdnE25 BLi4g7MrF3NwDmVfxkWJH1Eu4uCcyoUZP0X8qPKTjJ8g9lEuBH6cOJeNC4ILEOe28WPEeZTzg/OB 8xLntXEecG5ivb4hF9iHOL/yo+Cc4EeIH7NxDnB24gLK2cBZiQsqe4OzgDMTP66cCZyRuJByBrAJ NoifUL5nJvdf4D+Jn1Tlu+A/iJ9S5d/Bv4FvExdW5V/Bt4iLqPJN8A3wNeKiqnwV/DP4J2JfVf4R /ANxMVW+DL4E/pa4uCpfBH8D/pq4hCp/BT5LXFKVz4BPgb8kLqXKJ8DHif1U+Rj4M/AR4tKq/Cn4 EPgg8dOqfAC8j7iMKu8B7wbvIi6ryjvA24mfUeVE8BbwJuJyqrwRvB68lri8Kq8GrySuoMrx4KXg JcQVVXkReAFxJVWeB54DnkVcWZVngGPAU4n9VXkyeCJxFVWOAo8HjyGuqsqjwCPAQ4mrqXIkeCBx gCoPAIeDw4irq3IoOIS4hip3B3cFdyauqcodwG3BrYlrqXIL8DvEtVX5bfAb4KbEgaocBH6ZuI4q NwY3AL9AXFeVnwXXBdcmrmda54S6GrH+Wf7giuDyxM+Z1muWujS4JPHzptWmUhch1n/bk+DHwY8R v+ha40idm7i+aY2BqHOAsxLrc50ZnAFsEDc0rTkF9R/EjUzXnIr4F/ANYn3tr4J/Im5iWjEB6u/A F4lfMq2YDPU58GliXRdPgr8gfsW0YoTUR8CHiHVdPwjeD95D/KppxcipdxC/Zlo5BOqt4E3E+rW3 EbyO+HXTyllRrwTHEzczrRwg9RLwQmLdFswHxxK/aVo5ZOqZ4OnEb5lWzp16CrFuiyaBo8FRxM1N a00G9VjwaGLd9o0EDyd+17TW4FBHggcTv2daa5CoB4D7E+u2OBwcRtzStNaIUYeCexG3Mq01ctQ9 iHVf0B3cDdyVuI1prTmk7gzuRKz7no7gDsTtTGtNJnU7cFvi9qa1hjQ1676vNbiVgzua1hpYJ7cg 7sRY98XvCdxF6K6Mg4XuBr8/uruNWzq4B5xfO9PrEwLXD90Trn9PqB89of70gvrVC+pfKNTPUKi/ oVC/e0P97w2vj97w+ukDr68+8PoLg9dnGLx+w+D13Rde/32hfQiH9iMc2pdwaH/6QfvUD9qvftC+ 9Yf2rz+0jwOg/RwA7esAaH8joH2OgPY7Atr3gdD+D4T+YRD0H4OgfxkE/c9g6J8GQ/8VCf1bJPR/ kdA/DoH+cwj0r0Og/x0K/fNQ6L+HQf8+DPr/YTA+GA7jh+EwvhgB448RMD4ZAeOXkTC+GQnjn5Ew PhoF46dRML4aDeOv0TA+Gw3jtzEwvhsD478xMD4cC+PHsTC+HAfjz3EwPh0H49fxML4dD+PfCTA+ ngDj5wkwvo6C8XcUjM+jYPz+Pozv34fxfzTMD6Jh/hAN84uJMP+YCPOTSTB/mQTzm0kw/5kM86PJ MH+aDPOrKTD/mgLzs6kwf5sK87upMP+bBvPDaTB/nAbzyw9g/vkBzE9jYP4aA/PbGJj/Tof58XSY P8+A+fUMmH/PgPn5TJi/z4T5/UyY/8+C+MAsiB/MhvjCbIg/zIb4xByIX8yB+MZciH/MhfjIXIif xEJ8JRbiL7EQn5kH8Zt5EN+ZD/Gf+RAfmg/xowUQX1oA8acFEJ9aCPGrhRDfWgTxr0UQH1sE8bPF EF9bDPG3JRCfWwLxuyUQ34uD+F8cxAfjIH64FOKLSyH+uAzik8sgfrkM4pvLIf65HOKj8RA/jYf4 ajzEX1dAfHYFxG9XQHx3JcR/V0J8eBXEj1dBfHkVxJ9XQ3x6NcSv10B8ew3Ev9dAfHwtxM/XQnx9 LcTf10F8fh3E79dDfH89xP/XQ35gA+QPNkB+YQPkHzZCfmIj5C8SIL+RAPmPBMiPbIL8ySbIr2yG /MtmyM9shvzNFsjvbIH8zxbID22F/NFWyC8lQv4pEfJTiZC/2gb5rW2Q/9oO+bHtkD/bDvm1D22c E0zzdzsgv7cD8n87IT+4E/KHOyG/uMvG+cA0f/kR5Dc/gvznbhsXBNP86h4b0/zsXsjf7oX8Lnof 5If3Qf4YvR/yz+gDkL8+APlt9MeQH0cfhPy6nWl+/hPI39uZ5v8P2ZiuH/jUxqUdfNjGTzv4CKyP QB+F9RWcP4P1G+jPYf0H52OwvoTzcVi/gv7CxhUdfMLGdP3NSQ9M1/d8KbTu+/wdfNrGVRx8xgPT 9VNnGZ9zuZbrfer6/fUFDCsm9Y5ef6m+/pzXP+9jx/9HTdeBfcX4vAem69S+FvobG9N1dBeEvshY jzlqCPyd0JdsTNc5Xhb6e8Y/eOBk6zyF/onxFaH1mKy2wFcZXxP6OuMbNg508E2hbzH+RehfGd8W Wo9Z6wj8O+M7Qv8h9F3Gfwr9F+N7QusxeV2BTcZeQmdgnFHoTEJnZpxFaG+hszLOJnR2xjmEfkTo nIz1nKiewD6McwmdW+g8jPMKnU/o/IwfE7oA44JCPy50IcZPCP0k46eELix0EcZFhfZlXEzo4kKX YFxS6FJC+zEuLfTTjMsIXVboZxiXE7o84wpCVxS6EuPKQvsLXYVxVaGrMQ4QurrQNRjXFLoW49pC Bwpdh3FdoesJ/Szj54R+nvELQr8odH3GDYRuyLiR0I2FbsL4JaFfFvoVxkFCv8r4NaGbCv0642ZC v8H4TaHfEvptxs2Ffkfodxm/J3QLxi2FbiV0a8ZthG7LuJ3Q7YXuwLij0J0Ydxa6i9BdGQcL3U3o 7ox7CB3CuKfQvYQOZdxb6D6Mwzw05kXOuPI14V7WmIPeU9iP3AP4fu9h7P5Yq37IGq+UfpD3MDbu 8x7GI1z9D+1bm9mcq2Gufk/3lW+mn6u/3cLhXI1y9QVp8VwdhXN1NJVzddh1rj5Pw+dKv++Znitt u3Ol32+tz5Vec5pWz1UXOFddUjlXnVznKjgNn6sEOFcJqZyrDa5ztTkNn6uMXsnPlbbdudK5M32u dI4qrZ6rIK+UYwa7c/Wy1z9jhvs5V/9Xe1b8W7//v1WXCrjKtE6YMA7SY+bc5Gv5XeXCOv6hYwqu +73ruZm+r7feiyap3tW9VK/Z8e/quX+G/rWaQD285/oI0rF6Vcv035Y1vQ48VHXgqId14GNXHThh UweOelwH/NPrwENYB/Q41ZM6oN9TpeuAvr8N1gH3z+DrQKX0OvAQ1oEuHtSB113vJdd1oJtNHXD/ DJOpAxXSr/9Dd/0TPLz+a13Xf4vN9U/w8PpXSr/+D931z+jl2fW/57r+WbxSXn/3z+Cuv3/69X/o rn+Qh9df56A7u+aDeP2DPLz+VQXX/39hnt3QgHUCOlZqpJxn19c5b32OjbSbx8BzVdewz/kEutbD pPVztddMfq607c6Vfs9hY9d7+9LquWoE56pRKueqgetcNUnD5+qwkfxcHTbsz9UhV3t11Ei756op nKumqZwrd9vezEiPod7v9/vZfN6TPamHZ7COB7sntbeP3kf62l9+ZsQ9P1M/xnhvN/xUeX/FCmaD LCWMbpkmRmTMn+3syS1+RrT63I7nivno3/PWVV+jljpyqO+NLZ5oeKtyi8bePjG/WXtRB7UpYUSo zwV4hfbWZf0RrRz447G++tH6mBiR3XUu3M+pnz/xqrUndd1x5VPsSX3kaso9qa9ddd6TOq/NntQ6 HnS/e1L/f41xq7rGEk5jXH0ftlKutc3VXWsq6RjX/TMyOIxxX0/628r9HefIaDPevd967P74b9Tj 0Xf9zLx/+pn6UdejHXdT1ONzWI/XX/c17qr6sfCuVY/3X0tej3V9bdAqNKmcWf1VATd8jaDrVj3W j1iP3c+pnz/iulWPvaNS1uPo6ynr8errzvX42PWHY2/19DZWXjeL3PEz49WhH3XdeOtOirr5VWpt bK079m2srhNJ97dTT+Cj6q0+9gXt6XtEHXZtrPs5aRu7MDq9jcU2Vs9BPGlj9X1oqrvud4FtrP4Z nrSxFf9lbWzE/EDTe0GgqR91PVqvHqEen0+tjY1R32vXxurzqutN0aQ7+6k6o77/Xq38Pvpzdm2s +zlpGxs8Ob2NTettbN5YVb/UoR913WgSm6Jufp1aG1shNvCBtLHu56RtrPe09DYW29hGHraxdVxt bDObNraRh21spX9ZGxs/O9AMmBNo6kddjy7OTlGPv0mtjd0/+8G0se7npG3skZj0Njatt7EnlwWa 7ZYHmvpR1w2f5Snq5oXU2thbyx5MG+t+TtrGBs9Mb2OxjdUxT0/aWL0/s25jTxkp21j9MzxpYyv/ y9rYkLhA86469KOuR3FxKerxxdTa2PFxD6aNdT8nbWP956S3sWm9jfVeHGhOUYd+1HWj7uIUdfPb 1NrY4osfTBvrfk7axh6JTW9jsY1t6mEb28DVxrawaWObetjG+ju0sf/rOSq6zn+8V0o3NJKvT0Db vZewvuuIYt5LKG0jrkD/lej14NsI/3WB5g516Ef9Gg1el6KN+A7biN6qT0hUr72gdVYbMRr6rxyu /ku/hn1I/6Lrlw/pvzK7zoX7OfXz13L1X7cWpmwjgmz6rxCm/5qS3n89NOtqfZk2Tu/lccP4556p JYyU62r1zyjo0MZFqvKzRnujk3p9tDe6G6HqVadL7YzSRln1176pysHqs53U59uoUh/l0ur/5FRH 9n/+tr/L2ZPyNck/l9l17vSRy/X5TPB113lJ9jPS69d/t34FeNCH6v06ShrW3kE1bepXgAd9aJDx vPGiq4/J6XqOB3Fu3P3NBC/rHinoB9uH3ruvPrQlrEvj3Ipxa6HbMG4rdDuh2zPuIHRHxp2E7ix0 F8ZdhQ4Wuhvj7kL3YBwidE+hezEOFbo34z5Chwndl3G40P2E7s94gNARjAcKPUjowYwjhR7CeKjQ w4QezniE0CMZjxJ6tNBjGI8VepzQ4xlPEDqK8ftCRws90Uh+r2b0JKEnM54i9FShpzH+QOgYoacz niH0TMazhJ4t9BzGc4WOZTxP6PlCL2C8UOhFQi9mvEToOMZLhV4m9HLG8UKvYLxS6FVG8r0POK9m vEbotUKvY7xe6A2MNwqdIPQmxpuF3sJ4q9CJQm9jvN1IvncJ5w8Z7xB6p9C7GH8k9G6h9zDeK/Q+ xnq/5NoCHxD6Y8YHhf6E8SGhPxU66f1UDj4i9FGhP2P8udDHGB83ku9VxfkLoU8wPin0lzame32d Evq00GcYn/XAdC+0c0J/xfi80Hr/8gAHfyP0BaF1jqWag78V+jvGl4zke/Fxviz09zamew7+IPSP HpjuifgT4ysemO7J+DPjq0JfM5LvGcn5uo3pHpU3hL5pY7pH5i2hfzGS78nJ+Vcb0z1Ab3tgusfo b4x/t3FZB9+xcRkH/2FjuufqXaH/NJLv6WpnukfsX4x1VqmUwAbsYYs2YQ9czl6wh66d6R68GRhn hD197Uz3BM5kY7qHcGYbF3ZwFtjD2M50z2NvG9M9k7PauJCDs8GezHamezpnhz2f0Tlgz2g70z2m H4E9qNE5Yc/qnLDHNfpR2BP7UdgzG+0De2z7wB7cuWycE0z39M4Ne4Cj88Ce4XlgT/E8sOd4XtiT 3M50D/N8sMd5PtgDPT/skZ4f9lDX9qJ7wdnYBNM92gvAHu4FYI/3grAHfEHYI74g7CH/uGntp0lN 95wvBHvSF4I96wvBnvb6ntS/gG+BbxI/aVr7qVJfM5Pf+/oq+GfwFeLCprXfLPUPxPpe2d+DL4Mv ERc1rf16qS+CLxD7mtZ+xNTniYuZ1n7J1OfAZ4j1PRJPg0+BTxKXMK19sKmPE5c0rX25qT8DHyUu ZVr7klN/SuxnWvumUx8EHyAubVr3jqHeC95N/LQqfwTeSVxGlT8EbwcnEpc1rXvOUW8ifsa07mFH vQG8jricKq8BrwKvJC6vyvHgZcQVVDkOvBi8kLiiKs8HxxJXUuU54FngGcSVVTkGPA08hdhflSeB o4mrqHIUeDx4DHFVVR4FHgEeRlxNlYeABxEHmNZaJer+4HDi6qrcBxxKXEOVe4K7g4OJa5rW2irq juD2xLVUuQ24FXFtfc928Dvgt4kDTWvNFvXrxPp9fa+CXwE3ofc7MuH+R6pcH/wCcT1VfhZcl1h/ rTa4BjiA+DnTqjPUlcEViJ83rdcgdRli/bv6gUuCixG/aFptPvVTxPpcFAIXBOcn1veIygvOBc5J 3NC0xnjUWYn1tckMzgg2iRub1pyC+i6xvvZ3wLfBt4hfMq05LPVV8BXil00rhkB9mVjXxW/BF8Dn iYNMKwZFfRr8JbGu+yfAx4hfM62YJvVh8CHipqYVI6beT6xfe3vBu8G7iPX7bT8EbwNvJdav9c3g BOI3TSvHRL0OvIb4LdPKwVGvINZtzXLwUvAS4uamlXOlXgCeR6zbtrngOcTvmlYOnXoGeDrxe6a1 hoB6GngKsW5rJ4MnErc0rTUb1FHgCcS6LR8PHkvc2rTWzFCPBo8i1n3FSPAI8HDitqa1Bol6KHE7 01oDRR3pYN13DQYPIu5g44HgCOKONh7g4E427k/cWeguQndlHCx0NxvTv6+7B6bnr4eNB4Lp9Qmx Mb2+PeH625nWn15Qv3pB/QuF+hkK9TcU6ndvqP+94fXRG14/feD11Qdef2Hw+gyD128YvL77wuu/ L7QP4dB+hEP7Eg7tTz9on/pB+9UP2rf+0P71h/ZxALSfA6B9HQDtbwS0zxHQfkdA+z4Q2v+B0D8M gv5jEPQvg6D/GQz902DovyKhf4uE/i8S+sch0H8Ogf51CPS/Q6F/Hgr99zDo34dB/z8MxgfDYfww HMYXI2D8MQLGJyNg/DISxjcjYfwzEsZHo2D8NArGV6Nh/DUaxmejYfw2BsZ3Y2D8NwbGh2Nh/DgW xpfjYPw5Dsan42D8Oh7Gt+Nh/DsBxscTYPw8AcbXUTD+joLxeRSM39+H8f37MP6PhvlBNMwfomF+ MRHmHxNhfjIJ5i+TYH4zCeY/k2F+NBnmT5NhfjUF5l9TYH42FeZvU2F+NxXmf9NgfjgN5o/TYH75 Acw/P4D5aQzMX2NgfhsD89/pMD+eDvPnGTC/ngHz7xkwP58J8/eZML+fCfP/WRAfmAXxg9kQX5gN 8YfZEJ+YA/GLORDfmAvxj7kQH5kL8ZNYiK/EQvwlFuIz8yB+Mw/iO/Mh/jMf4kPzIX60AOJLCyD+ tADiUwshfrUQ4luLIP61COJjiyB+thjia4sh/rYE4nNLIH63BOJ7cRD/i4P4YBzED5dCfHEpxB+X QXxyGcQvl0F8cznEP5dDfDQe4qfxEF+Nh/jrCojProD47QqI766E+O9KiA+vgvjxKogvr4L482qI T6+G+PUaiG+vgfj3GoiPr4X4+VqIr6+F+Ps6iM+vg/j9eojvr4f4/3rID2yA/MEGyC9sgPzDRshP bIT8RQLkNxIg/5EA+ZFNkD/ZBPmVzZB/2Qz5mc2Qv9kC+Z0tkP/ZAvmhrZA/2gr5pUTIPyVCfioR 8lfbIL+1DfJf2yE/th3yZ9shv/ahjTOAaf5uB+T3dkD+byfkB3dC/hC9C/KPuyA/uQvylx9BfhO9 G/KjuyF/uhvyq3tsTPOzeyF/a2ea/90H+WE70/zyfsg/ow9A/voA5LfRH0N+HH0Q8usHIf+O/gTy 93am+f9DNqbrBz618VMOPgzrF+xM1z8csTFdP3HUxr4O/gzWb6A/t3FxBx+D9SWcj8P6FfQXZvL1 L5x1X+Ln4JM2Lu3gL83k6384n7IxXX902gPT9U1nPDBdP3WW8TmX8Z4s77nee6r7Rr0vivt97PT/ lfNK3V/ZmK4jOy+0vp9FBYG/sTFdR3dB6Is2puv8vhVajxkqC3yJ8WUb+zv4e8Y/2LiKg38U+icb 03WoV4T+WWg9Zqrm4GtCX2d8w0y+jpjzTaFvMdZjuuoC/8r4ttC/2biGg39nfEfoP4S+a2O6jv9P of9ifE9oPeaVWI+JaznYS+gMjDMKnUnozIz1mLy2wN5CZ2WcTejsjHMI/YjQes4Q6OBHhfZhnEvo 3ELnYZxX6HxC52f8mNB6TlPHwQWFflzoQoyfEPpJxk8JXVjoIoyLCu3LuJjQxYUuwbik0HoOVVdg P8alhX6acRmhywr9DONyQpdnXEHoikJXYlxZaH+hqzCuKnQ1xgFCVxe6BuOaQtdiXFvoQKHrMK4r dD2hn2X8nNDPM37BK/l9dji/KHR9xg2Ebsi4kdCNhW7C+CWhXxb6FcZBQr/K+DWhmwr9OuNmQr/B +E2h3xL6bcbNhX5H6HcZvyd0C8YthW4ldGvGbYRuy7id0O2F7sC4o9CdGHcWuovQXRkHC91N6O6M ewgdwrin0L2EDmXcW+g+jMM8NOZFzrjyM+FezvvF03vV53TdE9hwxxbU8R9bq3w2oPMAAP== In this particular instance, the Welsh distribution has heavier tails and is less peaked then the Behrens distribution. Since the standard errors for both methods are calculated the same way, for most alpha values the Behrens distribution will yield smaller confidence intervals.H4sIAAAAAAACC+3dCXwURfYH8K6RIwhqUHBh1eUQJK4KAQEREEFRZFGJrgeLyqGg3DIkhityEy7B IIcR5JBD7vs+REQ5VFQQBAW8Wa/V5VhdcZdd/vUyNX9e/6amqot/3D9sJp9P0/NNhumk+vWrqtfd M8LzvAFyqSKXZLmMCXleH7lEv3be5Xmj5FL+trtu9zzhVZrreecVk4v82fly6RJ9YmHP2yy/2UN4 Xmnh+b7SZhf2kuoW8pp4Pby2Xnevg9dI/ts972eV5VJCLkny14g+Lswe4/fvlevugn4Tzzt66tQp vp2cyHZFUflPI7mtjnJrXbwz/UrJ+3dGUoWdpeUrNykqNnc/VtG74eObetJjaqLcDZXznvOA/B5r Mq/ySs87eaSi1+eO/S3HyKV+yQMtqb2Sjlf0fm61v2Xy0Yp5z8u6f3/LH9XfUlItF8ulbN5P/X/b xsgGxMPy/9atdLznwuSr89quTOeUvD1H6+7yZxuuPN6zRN5TK+ws6y0VOfJ7d8vv0d8RbdfSeS0l 8v7fSvnzRl8f6xn9O+nnLeXSLpOa/vT+EezxBYb9c6bPD/r9ZnLdUC6pEXvl1baEit+mahkt2+uB UKzjvW5d9ZhiurVc6sglpNYeW9OWRJyIib4e/b9Sp/92r15ke95l6nek1/9cLrUDuo3FbR39qMWP Obqdo9tb/Lijn7C4g6M7OrqTxp8xd3Z0F0d3tbibo5+0uLujw47uYXG6ozMsfkounzo409E9Le7l 6N6O7mNxX0dnWfy0xp8Y3M/R/S0e4OiBFg9y9GBHD5HLxwYPdXS2xcMcPdzRIyweKZdDDh7l6Gcs Hu3oMRY/K5eDDs5x9FiLn3P0OIvHy+WAgyc4eqLFzwfwR8y5jn7B4kmOnqzxh8wvOnqKo6dqvJ95 mqOnW/xSAO9jnuHomRbPCuAPmGc7+mWL52i81+C5Fs8L4D3M8x29wOKFcnnfwYssXqzxboOXOHqp XHYZvMzRy+XynoNXWCyn/967Dl5l8Wq5vOPgNRrvNHitxevk8raD11u8QS5vOXijxm8a/IrGO5g3 OfpVuWw3eHMAb2N+LYC3Mm+x+HW5vOHgN9T3gnqrxluYtwXwa8zbLd6h2szkV5nfDOBNzG9Z/LaK maDeqWIwnt9RMR3U76pjxuR1zO9ZvEsd0yavYd4dwKuZ39d4FfMejVcavFfl1Hj+QOPlBu9TOd/k pcz7NV7C/KHGiw3+SPWR8XxA9bEmL2A+qPF8gw+pMUQ8f6zGJNxzDP5EjYlMns38qcazmD/TeCZ4 BvPnGr/E/IXG0w3+Uo2BuacafFiNweP5z2pMzz3Z4K/UnIL7BeavNc41+Bs1R+KeaPC3ao7GPZ75 O43HgZ9j/ovGY8E5zN9r/CzzD2rObfJo5r+qOX88H1E1A+6RBh9VNQzu4QYfUzUU7mzm4xoPBQ9h /pvGg5l/VDUokwcy/6RqYNz9Df67qsFxP838s8ZZ4L7MJzTuw/yLqmGa3Iv5H6qmanIm8z9VTTee T6oaMXe6wf9SNWrusMH/VjXyeD6lau7c3QymE1JdDRYics6Au7PBIRE5h2FyR+bzNO7AXEhEzsmY /DhzYY3bMxfRuJ3BRTV+zOAkETknFs/FROScWlCfLyLn7IK6uIicA4znEgHcivkCiy/U+BGDL3J0 ssUlHX2xxZc4upSjS0N7oS8NYL6/fhPAPD7KWFwW4k9nHs+/1ZgfD5fB8aMzPx4vh+NXZ378XwH5 4grIJ7+D/KMzz1/lIN+Vg3xYXvjzJ/lJMM/HFYQ/v5PTwby/qCj8/QmZ9z9XCn//Re4N5v1hJeHv T8lPg3l/XVn4+3cyHw9cJfzjB/JQMB+/VBH+8Q2Zj49ShH98RR4D5uO5q4V/PEgeB+bj0d8L/3iW zMfD1wj/eJo8BczH99cK//yBzOcf1wn/fIY8F8znX1WFfz5HXgLm89Fqwj/fJfP5darwz9/JG8G8 XlFd+OsnZF7vqSH89SXym2Be77te+OuZ5N1gXp+uKfz1fzI/X1NL+M//kT8Df8lcW0TmQNzfgr9n vkFExuzcx5nriMiYlvsX8EnmG0VkjMVNY56o64rIGIO7GLgEcz0R6fO4LwFfylxfRHIw9xXMN4lI juKuBK7C3EBEjgHuqsw3i0gMcNcC38jcUER+J+6G4FuZG8nHTcB/YL5FPr4bfC/4fmZ67T+BHwa3 YW5M/Rn4CebbqD8BdwP3YL6d8ju4NzP9rVngAeDBzHdQvgWPBI9hbkr5EzyBmdo2FzwZPI25GeVD 8MvMd8rH88ALwUuZ75KPV4BXg9cx075/BbyZubl8/Dp4G/hN5jTKZ+D3wHuY75GP94E/YqZYPAj+ BPw58x/l48Pgr5nvk4+/A38PPsJMsX8c/BP4Z+YH5ON/gE8yP0j5DSxCfhdibkH5DpzETMdicfAF 4IuYW0qXBF8CLs38kPRvwGWZ6di/DHwFuBzzI9IVwFeCKzG3kr4KnMLcWvpq8DXga5kpN1UFV2Nu K50KrgG+nvlR6ZrgWuDazJQLbwDXYW5H+R5cF1yPuT31BwY/Ln0TuIHBlJtvtrghcweLO0o3cnAn R3e2uIuju8Lvj+6m8c0GPwntqzPfP91h/6HDsP/DEB9hiJ8eEF89IP7SIT7TIX7TIb4zIP4z4PjI gOPnKTi+noLjLxOOz0w4fjPh+O4Jx39PyA+9IH/0gvzSC/JPb8hPvSF/9Yb81gfyXx/Ij30hf/aF /NoX8m8W5OcsyN9ZkN+fhvz/NPQP/aD/6Af9Sz/of/pD/9Qf+q8B0L8NgP5vAPSPA6H/HAj960Do fwdB/zwI+u/B0L8Phv5/MIwPhsD4YQiML4bC+GMojE+GwvglG8Y32TD+yYbx0TAYPw2D8dVwGH8N h/HZcBi/jYDx3QgY/42A8eFIGD+OhPHlKBh/joLx6SgYvz4D49tnYPw7GsbHo2H8PBrG12Ng/D0G xudjYPz+LIzvn4Xxfw7MD3Jg/pAD84uxMP8YC/OT52D+8hzMb56D+c84mB+Ng/nTOJhfjYf513iY n02A+dsEmN9NgPnfRJgfToT540SYXz4P88/nYX6aC/PXXJjf5sL89wWYH78A8+dJML+eBPPvSTA/ nwzz98kwv58M8/8XoT7wItQPpkB9YQrUH6ZAfWIq1C+mQn1jGtQ/pkF9ZBrUT6ZDfWU61F+mQ33m JajfvAT1nRlQ/5kB9aEZUD+aCfWlmVB/mgn1qVlQv5oF9a3ZUP+aDfWx2VA/exnqay9D/W0O1Ofm QP1uDtT35kL9by7UB+dC/XAe1BfnQf1xPtQn50P9cj7UNxdA/XMB1EcXQv10IdRXF0L9dRHUZxdB /XYR1HcXQ/13MdSHl0D9eAnUl5dA/Xkp1KeXQv16GdS3l0H9exnUx5dD/Xw51NeXQ/19BdTnV0D9 fiXU91dC/X8lnB9YBecPVsH5hVVw/mE1nJ9YDecv1sD5jTVw/gO9Fs6frIXzK+vg/Ms6OD+DXg/n d9bD+R/0Bjh/tAHOL23UuK3Br8D5LfQmjVsb/KrGrQzebPFrcH7Q5i2Oft3iNxy91eJtjt4ewLy9 dlj8psatDX7L4rchPmzeCfFn8zsQz+h34XjQmR8/7wUwPx53acyP390aP2Hw+5Av3od8skfjTgbv hfylM893H0A+RO+D/Kkzz7f7IR+jPxT+63N05vn9I8j/OvP+4gD0J+iD0P+Qexp8CPqvQ9C/oT+G /pDMr7/6RLm+uk+d7q8v40WO4Yfo+kuaD4RO38fO/18WmPfLn2rMryP7DPp1nfk4gObgA8GDDP4C xhlkfh3dlxoPBfPr9A5rzMc5f4ZxkM78OsKvYBylM79O8WsYh6G/Ef7rIL+BcRz6Wxj3kfl1mN9p PBbsu85T43Fgfh3p9xrzcesPwn+dqs583PtX4b8OVmc+bj6iMb8O9yiMu3Xm1/keg3E7mmpUUy3m 84C/Cf91yjrz65x/1JjPM37SeCaYz1P+rjG/jvtnjV82+ITwX0euM59H/SL816mjqUY432I+T/un xgsNPgnzPvS/hP86f535PPLfGvP7DE5pvMxgeqOR5Rbz+ySExaGQf16sM7+P4zyN+X0ghTReY3Bh jdcaTDXndQYX1Xi9wVTT3uDgYiF/3QF9fsh/n5DNVGPfZHAJjV81+AKNNxt8YchfZ0FfpPEWg5M1 5veRlXT0xSF/XchmOuex1eBSGm8zuLTG2w2+1GI6Z7PDwWU05nW0sgHM76P8raPpHNTbBl/uaDrH tdPg3wUwv8+1nKPLh/z32aIrOLpiyF/3RF/paDqHuMvBlS2mc5S7HVwlgPl93ikWX+3o34f896mj r3H0tRrvNfg6i6sGMH+fgGoWpzq6usb7DK5h8fWOrqnxfoNrWVzb0TdozN8Ho46jb3R0XY35+4DU c3R9i29ydAONDxh8s8UNHd3I0beE/O9Dg77V0Y0tvs3Rtzu6Scj/PkHoOxzd1OI/OLqZo+8M+c8T ou9y9N2Obm5xmqPvsfjekP99umz+o6Pvs/h+Rz9g8YOObhHA/H3e/mRxS0c/5OiHLX7E0a0sbu3o No5uG/Kfp0c/6ujHLG7n6PaOftziJxzdweKOju7k6M4a8/cB7eLoro7uZvGTju5ucdjRPRydbnGG o5+yODOg8bxI9PxKr1Dkuhr+nsIp3un3AD7T9zCOfi2XL7IsFOuz4T2Mh6r+h/etZGyrwarfo77y wVCiraJuZWirYaovKIhttRvaanectnpPtdWeAtxWdN8zbyuyrq3ofmtqK7pmsqC2VSdoq05x2qqD aqsuBbit1kBbrYnTVqtUW60rwG1VKORvK7KurejcGbUVnaMqqG2VFoodM+ja6u7Q6THDmbTVf+oz K87V5/9asVRGPeYxIWAcRGPmi9nPLlWPy1H9g2oK6r2maG5G177QZ9HkxV3Drxvd/8FXjaKvQb/W nRCHp9RXGtXqZZTR31YsEQNnVQzsDhgDb6kY2K+Jgd2BY6BmIgbOwhigcWqQGKD3PaIYoHt/MAai r2GPgRqJGDgLY6BTgBi4T91LTjHQVRMD0dcQlhhITez/s27/rwm4/5er/b9es//XBNz/NRL7/6zb /zRPCrL/T6n9XzQUu/+jr2Hb/zUT+/+s2/9pAfc/nYPuqOaDuP/TAu7/2g77/79hnt3U87+fA7m5 5jxGEzonT22srrUsiDUJbKuGythWDdT1sgW9rd4Q/rYi69qK7mFspu4VLKht1Qfaqk+ctuql2iqr ALdVNWiranHa6jrVVtULcFsd9vxtddjTt9UXKrd/5RXctpoEbTUpTlvlqrZ6sQC3VXNoq+Zx2io6 ZrjHS9Tmz/T5KZrvB/ms8yHnRZb8/azzpGT6fPISC7NFrlzy1kmbvMZyvaN6qrijaGWva+GxWdVK nj//w/UpXo783uZbr0ym3/PHIxW9+nJJkc+dXmmjlyQft2qWlJx7IvIZ52mPVvay5PfqhNIz6DF9 5Ug3+MvenrSOfI3NKq7aIrpN2v7GI5HPOm8xpWrMZ53vOhL7WedHj5g/67yU5rPOqc54pp91/v81 d6qtxqimuRPd315F3TN5o7q3g8+doq9RxDB3apFXP031qsqlhlyiddRCal1MM68607iOfv0acT1r XrZInZ8taE1xdWheTFwvwLheeayid1LGy+Z5kbjecdQf1xS/d7RJz3tcRP5VdY5X9NKOReKa1hjX 0W3S9rOOReI6dXpsXOcci43rpcfMcb33WGxct/w/xHUi5/7ncm79OTIu5EJrio2MOTGxuTBezm0x R59zKSby3kdRbiBZxi0t29O29twlF13OjW6T59ydMxI5F3MuzXWD5NzFKuceFLE5l14jaM6t7tU6 Z3Pu2l5h0bh3WNCa4uqoXENcL4qXc/fK5+pyLrUzxVGFvHd3lDEkn3+q/qXJ9D1dzo1uk+fcWbMT Obeg59y0zLA4JBdaU2wMz4yJzcXxcm6XzHC+5NzoNnnObTg3kXMx5/YJmHPbqZw7VpNz+zjl3HN3 nPtNelhkZIQFrSmuymfExPWSeDm3UEb+5NzoNnnOLbMgkXMLes49MSAshgwMC1pTbKQOjInNpfFy bqmB+ZNzo9vkOXflokTOxZxbLWDOLaty7u2anFvNIeemnsPj3Bb9wsLrHxa0prjK6RcT18vi5dyM fvmTc6Pb5Dn3maWJnFvQc+7RvmGRlRUWtKbYSMmKic3l8XJuiaz8ybnRbfKcm7IikXMx59I5PFPO 7aJyLr2fD+XcE15szj2sfm9Tzo1m3NRzNN8eHh4W3UeEBa0ppi4fERPTK+LlW29E/uTb6DZ5vj25 KpFvC3q+zcoOi6RhMudmR2JzZXZMbK6Ml29zs/Mn30a3yfNt7tpEvsV8Oylgvs1W+XaxJt9Ocsi3 tc7RfFtqiIxLudCaYurOITExvSpevk0dkj/5NrpNnm+7bEjk24Keb4dvzxB1BoUFrSk2Nss1xObq ePl2lnxufuTb6DZ5vk3alMi3mG+bB8y39VS+fUyTb5sHzrfVA41v/9uv5+L3Wj8TinVTz3+NOFr3 fi5N1DLG8n4urvniB+jLNobyP1+U35ohFsqF1nS8ttgaky/WYL7IkP3DRnkc1t8ayRfDoS8rofoy Op6TWV9D8ZXM+rIiqi2i26Tt11d9WZ0tsfkiTdOXdbf0ZeMTfdlZc29jRUu+m6vug41+flRlL/be RnqNiwz5jo6HW7z2Xgd5fLT3unnp8i+8Ti4PSnWRos9wuVAuxU//Hf/7uLhqkyJqXZJ9L/qcRIz8 ujFSxxIjbbzIZ3dfpe4NqKeJEXqN8wwxQq+T5jX2blf9xIWafctz9YWqX/HU70mP/weONnpHJKgA AK== This graph shoes the difference between the two probability density functions for the t and the Behrens distribution with appropriate parameters. While the tails do appear to asymptotically approach zero, their values are already close to zero in the tails of the distributions. Keep in mind that this graph should integrate, from -Inf to +Inf, to zero.H4sIAAAAAAACC+3dCXhU1RUA4PsuWxDEgICgKBC2uKCACIhxDC4sRWmKIoqIoKCsEgGNmrRuqFQj QkXBYilKRaioiCgIiCgiiCBG0YCgSNlLMSSGPZjek3lTzjtz5513+LANzeT7bt78M5N5mfvOnLfN Pc9RSj1sWjPTEk0bq5V60LTIz6rrlHratAbXXNdRKUcVTVVqeYJS5cxjp5g2NPLECkotMXeOcJSq 5SjPT9qrFVRC+/Kqkxqh+ql0NVB1ML/TSx5rYlpV08xLPhy5XQHdpvd3N9N0B/4TpfYWFxfj+YwL z9epZH51MPMaZOY2VB3vT3LJ75TaDQtqmVfuqRwnPT9Jtf3+8gy4DV00aWGTkufcaO5DXaaazFWq KC9JPdg5t9dY01Kqf9cL+iuhIEkd6JPbK3FvUsnzsnrk9ip030t1t9UwrW7Jo973tig8A6e3+dv2 jQsyZiWeW9J3dYYklyw5mKabxxY2KsioWvLUhgV11WxnnLmvm7kP3kekX2uV9JRT8ndzzeMdduRn RN4nPN7LtP73QdcfWz4Oun2qz/I53ucHvb+rmaaa1iJs1cCdl+PGbxe3PWP660Yd7Viv2969DTF9 m2ntTNPuVKEpzMmJETGR14O/q3nsvavLwvNTZ7n/I7z+raa1Qe5HfCdyX9MGEw9Hhr8dSZxBnIV8 u/uZxx6NfIdpY4izicch9zfteeIXif+CPMC0l4n/hgzvfQbxLOLZyHeZNpd4PvJA0xYSf0i8FHmQ aZ8SryRejQzLJod4LfIQ09YRbyDehAw56x/E24h3IQ8z7V/Eech3m1ZAvJ/4EDLEVhFxMTJkbu14 XYE4Afke06oQVyOujjwCPj/EZyBDrJ9JfDZxfeRRpiURN0G+F7I98XnEzZHvg/xD3Ir4EmT4LLYl bo98v2mXE19BfCXyA6ZdTdyRuAvyg6Z1Je6GnAnraOLuxD2QIZf0JL4Z+fem3ULch7gv8h8gBxH3 J74T+SH4DBIPQYbcNox4OPE9yI9AzBDfi/woLDPiB4gzkR+D90j8EPEjyJB7HyUejfy4aU8QjyF+ CvkJyNfEzyA/adqzxOOJn0OGdcEE4heIJyH/EfI/8WTkp2B9QDyFeCry07C+IJ5G/CoyrKumE89A fsa0mcSvE89CHmvaG8RvIT8L6yPiOcTvIMO6813i94jnI4837X3iBch/gu1D4g+IFyM/Z9oS4o+Q J5j2MfFS4mXIsO7/lHg58QrkF2B9Svw58kTY7yBeTfwF8iTT1hDnEH+FDNsmXxOvRf6zad8Qf0uc izwZ1u/E65FfMu074g3EG5FhW+l74h+INyFPMe1H4s3If4XtCeItxFuRp8L2BvF2ZNh220G8k3gX 8ium/ZN4t4+nwfYM8R5k2Fb8iTiPeC/yqxbnExcgTzftZ+JC5NdM28d4PzJsyx4gPog80+JDxIeR /27aEcZFyK+bdtTHsG39C3Gxj99Q4Z0cbAf5TYs1cTnktywuT1wBebbFFZHfNq0S4wTkORZX9vE7 sJ9IXAV5rsVVffwu7Cf6+D3YXmZ8GvI8ixOJqyPPt7gG8vsWn+7jBRbXRF5ocS0fLzKtNuMzkD+w uA7y4gCui/yhxWciL7H4LB9/ZHE9H38M+zc+XmrxOT7+xOL6Pl4Gx1l8/KnFDX283OIk5BUB3Aj5 swBujLyS8eewfyjwKoubIq8O4GbIXwRwMvIaxl9afK6PcwL4POSvGH9t8fk+Xsv4G9MuEPhbi5v7 OJfxOosv9PF6xt+ZdpHAGwK4BfJGxt8HcEvkH4TexPhHOH4i8GbGcOzsYoG3CL3VtNY+3ib0dsY7 4HiSwDuF3mVxG+R/Cr1baDh22dbHe4T+iXFeALdD3it0PuOCAL4U+WfGhULvE3q/xe2RDwh9kPEh oQ8H8GXIRxgXCX1U6F8YF1uc4mM4IeVnR2gtdDnG5YWGcwmX+7ii0JWETmBcWehThIZzJSEfVxX6 VMbVhD5N6ETG1YWuwfh0i6/wcU2hazGuLfQZQtdhXFfoMxmfJXQ9oc9mfI5xqsD1GTcQuqHQSYwb Cd1Y6CaMmwrdjHGy0OcKfR7j84W+gHFzoS+0uIOPL2LcQuiWjFsJfbHQrRlfInQbodsybif0pYzb C32Z0CmMLxc6xPgKoVOF7sD4SqGvEvpqxtcI3ZFxJ6E7C92F8W+E7sr4WqGvE7ob498KnSb07xh3 F/p6xjcI3UPoGxn3FPomxjcL3UvoWxj3FvpWofswvk3ovoz7CX270Hcw7i/0AMZ3Cn2X0AMZDxJ6 sNBDGA8Vehjju4UeLnQ643uEHsF4pNCjhL6X8X1CZzC+X+gHhH6QcabQWUL/nvEfhH6I8cNCPyL0 o4wfE3o048eFfkLoJxmPEfqPQj/F+Gmhsxk/I/RYoZ9lPE7o8Yz/JPRzQk9g/LzQLwg9kfEkoV9k /GehJwv9EuO/CD2F8V+Fnir0y4xfEXqa0H9j/KrQ0xm/FsD4+N4MoWcy/rvQrzOeJfQbQr/J+C2h ZzN+W+g5Qr/DeK7Q7wr9HuN5Qs8n50+o3xd6gdALGS8S+gPGi4X+UOgljD8S+uMAxucvlzL+ROhl jD8VernQKxh/JvRKxp+T8+ucVwm9mvEXQq8R+kvGOeT7FZy/Yvy10GuF/obxtwGMvz+Ty3id0OuF /o7xBovb+3ij0N8z/sF1ijtOHcbX13HHqN/iji26Sh8bx07/LpY3WYy/R/aj0JuF/gfjLRa38/FW xtuE3m5xWx/vYLxT6F2MS8ZsCbxb6H9ZjL+Hukfon4SGMWOtfbxX6HzGMMbsYoF/FhrGqLXy8T6h YQxbSx8fEPqgxS18fIjxYYsv8vERoWEM3YU+PhrAeJzAL4yLAxiPY4AxeBLDmLzzfawDGI/jKMe4 vMXn+rhCAONxLBUZV7K4mY8TLG7q48oW43FApwgNYwYb+7iqxY18fKrFST6uZjEep3VaAONxYImM YcxhfcZ4nFqNAMbj4E5nDGMQ6zHG4/RqBTAeB1jbYjyO8AyL6/i4jsV4nGNdi2v7GP63WozxOM2z LMbjPOsFMB5HerbFeBzqORYnEuNxrvUtruZjiMVTfQyxXZUxHuebZDEeJwyfxcqM8TjkxhZX8jHk korEeJx0U4vLE+Nx2M0s1sR4nHeyxXicOORyPI7cZjwOHdYdR30M66Yi4iM+hnXhYeJDxHgcfnOL 8Th+WNfvJ97nY9i2KCTGdQZgW6aAOJ8Y1zFoaXEeMa6TANt2e4hxnQXYltzNGNdxgG3bXcQ7iXGd CNj23k6M60zAvsBW4i3EuI4F7KtsJsZ1MGDfahPxD8S4zgbsC24k3kCM63jAvu16YlwHBPbpc4m/ JcZ1RuAYxlpiXKcEjul8RZxDjOugwDGwL4hXE+M6K3AM8nNiXKcFjjGvIF5OjOvAwDmUZcRLiXGd mSu1tw4NGNepgWMQi4k/IMZ1cK7W3jo5YFxH5xrtrbMDfo8Y1+npqL11fMBziHEdoE7aWycIjOsI ddbeOkPg14lxnaIu2lvHCIzrHP1Ge+sggacR4zpKXbW3zhJ4CjGu03St9tZxAuM6T9dpbx0o8AvE uI5UN+2tMwUeT4zrVP1We+tYgXGdqzTtrYMFHkOM62j9TnvrbIFxHa7u2lunC/wQMa7zdb321gED P0CM64jdoL11xsC4DlkP7a1TBh5OjOucQX3LIcS4TlpP7a2jBu5PjOuw3aS9ddrAfYhxnbebtbcO HBjXieulvXXkwN2JcR26W7S3Th24KzGuc9dbe+vggXGdvFu1t44e+ApiXIevj/bW6QPjOn63aW+d P3ArYlwnsK/21hEEn0eM6xD20946hWBcx/B27a1zCD6bGNdJvEN76yiCcZ3F/tpbhxFcjRjXcRyg vXUewRWIcZ3IO7W3jiQY15m8S3vrUIL3E+M6lgO1t84lGNfBHKS9dTLB24hxnc3B2luHE7yB2FPH U5M6n9pbB3So9tYJBa8kxnVGh2lvHVLwh8S4jund2lvnFIzroA7X3jqp4FnEuM5quvbWYQXjOq33 aG8dV/CLxLgO7AjtrRMLzibGdWZHam8dWjCuUztKe+vYgjOIcR3ce7W3Ti4Y19G9T3vr7IL7EcM5 EHpeBLYR4bzI/Tq8jYZrCiejGsDHW8M48jPHvMjbOtqloYbx4+76B69be1jOIT3mrvdgXdkz3lf/ cR+fvnrSXReUxb7KIX2VE6Ov1rh99XUZ7isY99yDjIO29RWMt4a+gnHNZbWvBpO+Ghyjrwa6fTW0 DPfVPNJX82L01btuX71fhvuqvPb2FdjWV3Dc9Hr3+GxZ7as0Hb3NYOurbvrYNsPx9NV/65oVJ+vz f61YquPexjHhkO0g2GaugR6r7d6uD8c/4JiCW+8d9s2grjdci6Yk7lJ3dOjxzfYOkdeAf+taEofF 7k8aHKs3UQbvrXI8BkpVDOQEjIGVbgzkWmIgJ3AMtI7HQCmMAdhODRIDcKwKYgDq29AYiLwGHwOt 4jFQCmNgcIAYuMEdSz7IPc5NYyDyGg4TAy3iy7/ULf95AZf/HHf5L7As/3kBl3+r+PIvdcsf9pOC LP9id/lX0tHLP/Ia3PJvHV/+pW75pwVc/nAOepC7P0iXf1rA5d9GsPz/H/azu7jn+tsgZ1vOY3RS 4WstdXXP5ZfFYxK0r1Jd074Kud/HKOt9hb9vlura1lfwvbOu7piGstpXE0lfTYzRV8+7ffViGe6r EOmrUIy+SnH7KrUM9xX+DkOqa1tfbXFz+w5Vdvsqm/RVdoy+iqwHx6r48ebjfX6y5f4g1+8eXS7c Tuz1uxMS4ZrbW38OOemFIQemkxIWq3rm9oqWLZzOlZqoYRXGZ7WqfsqBdQuS1Thz35KrGiXC/1mY l6RSTFPmuVMbL1IJ5nafrgmJkw6Gr9uddnsTlWXua6dHjoLb8DPOOLR7bQZMwz/js6q4fRGZJ8x/ UV74+t1DVzWPun73l3nR1+/em+d//e6alut3w7Gz471+9/9qf6CNu93F7Q80c79ne6n7/U+8PxB5 jeM5HnS8sRv5+TViNys/5CQUhByYQuzMzY+K3YM0dufmJ6kiExOT8sOxu2KvN3YhRjv3HVlyu6J5 V+0KklRafjh2YUpjNzJPmH9Wfjh2k9dEx+64/OjYnZ3vH7tr80vHtefjeVUemzXzTHyZBlOIjWvz omLzUKy82iLPnlchJkrq/5kZJJq4heaXVyPzxHn1k5x4XqV5FfbRuHMtzdx6Ape646xpXoXX4M61 tDTvrvJJkltTi0LOKtNgCvFzf1FU/B6OlVt7F9lzK/QnxEvDklEIJlbM84tTaifCfbbcGpknzq2j 18Zza1nPresOhZz+h0MOTCE2Eg9HxeaRWLm18FDw3Lo8bVnGl6bZcmtknji3NsiN51aaWycGzK1j 3dw61ZJbJwbIra1OotyafiDkFJkGU4ifGQei4rcoVm7NPnBicmtknji3/rg+nlvLem4tfCXTmbAv 5MAUYiN1X1RsHo2VWxOnZZ6Q3BqZJ86tWRvjuZXm1lDA3HqJm1s7WXJrKEBuvfgkyq3ZUzOdOi9n OjCF+PnETEn8/hIrt86YmnlCcmtknji3pmyK59aynlsbT8l0ZpsGU4iN3lOiYrM4Vm5NnXJicmtk nji3rtscz600t8I5oyC5Fa4VDrn1JxWdW7cpPre2Poly66LJmU7nlzIdmEL8FE6Oil8VK7eum3xi cmtknji3Ttoaz61lPbfunJHpjJqZ6cAUYqPBzKjYdGLl1vIzT0xujcwT59bWO+K5lebW7IC59TE3 tz5vya3ZAXLrJTFy6//7OX08hixbR7uL8n73jdo2Tr2T28Yy49SluWEPWW8t0ic+Nzw8PdOp+lqm A1P4bM6fHpUbNM0No8y6YJH5zL00PZwbxpD1VlV3vQWf3US0XoH4SkTrrYpuX0TmCfNPcddbabuj c0OaZb2Vzqy3JsTXW6VmzEYSk9ugngjUpIlcF6OJih6zAa9xmk9ug8/DlWqAGmg+HwPU3WqkeYcX mdbTaKjRQPN4NdOqHHsf/7ldxe2TSKuO7os8Jx4jv26MtGNipK8KX5O0qQpfW+4yS4zAa5TziRF4 nTR1terorieqWZYtztXV3PWKcv9PuP1v6g3AbPygAAC= This graph shows the ratio of the density of the two distributions. Surprisingly, in the tails, the two distributions do not seem to be converging in their tails, but this far out the tails will represent extremely small p-values. From this view, it seems that the Welsh t distribution best approximates the Behrens PDF around 0.H4sIAAAAAAACC+3dB3QVVbcH8DmhhR6qFBEIXXoR6VUpAgoKgkjvvTcxCgpIx4AgRRBEEClKESkS EZAOShUQBUV6M4Te887J3Pu5szOZPX8W33v4kqw1uft3c3Mn98zOnjP1KMuyhuopn56C9DQhwLIG 68n/tbueZY3VU44X69WwLGUVu2tZDVJZVgL9s2R66uZ/YSLL2qCf7KMsK4Oyon3Vn5/ICiyX0Kpp 9bFaW72sTlZV/b1X1M/y6CmFngL1n+GPE5GYP/+qfuylzF9iWVciIyPpfELt+aok+ltVPa/Oem7d rEf9yh/1vWbGnHcy6HeumURt6BURbD1/rOJAE5smmrYuT9RrXtfPkSaz8qy0rPvhwdbgWoebTtBT hTRHm5r2CrwabN1qcbhp0JXgqNeFNDrc9Lrvs6TxTWn1lDnqp9E/W5g9A9VM/2653FcHLgkqENV2 mbrmj1py5rGX/tm6XFcHpoh6ac47ma1lKlQ/97J+znwOf7tmiGopFfV7K/XPq56NGOj/nObnTfXU boBp+n+WjyJxSpfl86iv9/p8Hf1YRU/FbFs5fPNSvvyt7ZvG6/Z6PSCmY3vfcr7Y5HRLPZXRU4Dv 0SKPZk7+9I5kGeN/P/N76f/57FZ5e35WVt/faN6/qn5RaY9uJbg16DaC24JuB7q94A6gOwruBLoz 6C6Cu4LuBrq74B6gewruBbo36D6C+4LuJ7g/6AGgBwoeBPot0IMFvw06RPA7oN/V003l3UMEDwX9 nuD3HUz/fu5hoIcLHgH6A8EjQY8CPVrwGNBjQY8TPB70BMEfgg4FPVHwJNAfCZ4MegrojwVPBT0N 9HTBM0B/Ingm6FmgPxU8G/QcwZ+Bngv6c8HzQM8H/YXgBaC/FLwQ9CLQix1chXgJ6K8Ef+3gyi5e CnqZ4OWgV+ipEuBvBK8E/a3gVXqqCHg16DWC14L+zsEViNeBDgP9veD1oH8w2/Au3gB6I+hNgn8E vdnB5Vy8RfBW0NsEbwe9A/ROB5cl3gV6t+CfQP8Meo/gvaD3eXAZ4v2CD4A+KPgX0IdAHxZ8BPSv go+C/g3074KP6el5wMdB/yH4T9AnBP8F+iToU4JPgz4j+Czoc6DPC74A+iLr/11k/S3uS4Ivg/5b cDjoK6AjBF8FfU3wdQdXcvEN0DcF3wJ9W/Ad0HdZf1PyPcH3QT8A/VBwJGhzQIqb9l8V6ADQCQQn 9GDaH00kODHoJKADVfT+IXdS0MlU9P6T5OSCU3gwXb+nFJzKg2l9T+3g0i4O0n7OxWlApxWcTrsU 4PQeXJI4g+CMoJ/SLgE4k4OLE2cGncXBxYizgn5auyjgbNpFXPyMBxcmzi44h3YhwDm1CwIO1n7W xbm08zPnc3FuB+d1cR4H5yHO6+DcLs7n4FzE+R0c7OIC2jkF5yB+VnBB7eyAC2k/4+LCDs7m4iLa TzNndXFR7SwuLqadmTmTi4trP8WckbiEgzO4uKR2euZ0zGmJSzk4DfFz2kGCUxOX1k7FnNLFz2un YE5OXEY7GXNSF5fVDmROQlxOOzFzIuaExOUdnIA5gLiCOTuL2SKuqB2povsh8wPiSjq+z3yPuLKO 7zLfYb5NXEXHt5hvMt8grqrj68zXiKvp+CpzBPMV4uo6Dmf+m/ky8Qs6vsh8gfhFHZ9nPsd8lriG js8wnyauqeOTzH8xnyCupeM/mf9gPkZcW8e/M/9G/JKOjzIfYT5MXEfHh5gPEtfV8QHm/cz7iOvp eA/zz8y7iV/W8S7mncSv6Hg78zbmrcT1dbyZ+UfmjcQNdLyBeT3xqzr+nnkd83fEr+l4DfNq4oY6 /pZ5JfMK4kY6Xs68lPlr4td1vIR5MXFjHS9kXsD8BXETHc9j/pz4DR1/xjyb+VPipjqeyTyDeTrx mzqeyvwxcTMdT2aexBxK3FzHHzKPZx5L3ELHY5hHEbfU8QfMw5mHEbfS8XvMQ4hb6/hd5hDmwcRt dDyIeQBzf+K2Ou7L3Ju4nY57Mvdg7kbcXsddmDsRd1D2RN2euS1xR2V/RuqWzM2JzbyaMTcl7qzs nKV+nbkhsfksrzE3YH6FuKuyaxp1HWLTVi8x12KuQdxd2eso6mrEZllUZa7MXJHYLMvyzGWZyxCb 8+tLM5ciNrlSgrkYc1Fic01AYeaCxCYXCzDnZ85L3E/Z2zzUwcw5iE3uZ2fORmz+V7IyZ2HORDxQ 2dvw1OmJzf9iOuY0zKmJ31L2PhbqFMzJiM3/fiBzEuK3lb3PjDohcwBxiO8Eemqzj5H6AfE7yt5n Sn2X2NSu28y3mG8Qm9p3jfkq8VBl72OnDme+TGxq6yXmC8znid9X9jEU6jPEpnafYj7JfILY1P4/ mY8Tj1D2MTXq35iPEpt1yxHmw8yHiEcq+5gp9QFis+7az7yXeQ/xaGUfo6bezbyL2KwrdzJvJzbr 1m3MW5k3E49T9jkM1JuIzbp7I/MPzOuJJyj7nBDqMOZ1xKavsJZ5DbHpW6xmXsX8LfFEZZ8DRP0N sem7LGdexryU+CNln1NF/RXzEmLTV1rMvIh4irLPOaP+knkBsemLfcE8n3kesenLfc48l3iass8h pJ7DPJvY9BU/ZZ5FbPqWM5k/YZ5B/ImDpzNPIzZ92anMHxPPUvY5sG6eTGz6yh8xTyI2feuJgkOJ 5yj7HGTqCS42ffnxzOOI5zp4LPMYYrOtMFrwKOJ5Dh5JPF/Z57S7eQSx2ZYZ7mKz7TNM8PvEXyr7 GgE3DyVeKHiRsq9h8GqzLfeui5c4+B0Xf6Xsazjc/Dbx1w4eTLzUg98iXubgQcTLPXgg8QoPHkD8 jbKvCYrNZtu8L2Czbd8H8CplXwMVm1c7uJeL1wheq+xrurza7NvoAXidg7sTh4H+3sHdiNeD/kHZ 19x59QbBGx3cxcWbQJt9V51dvBn0FsFmX1onwR2Jtzm4g4u3C97h4PYu3il4F2izb7Id4J8Em32f bQHvAb1X8D4Ht3HxfsEHQB8E/YuDWxMfAn1Y8BHQv4I+Kvg30GbffyvAxwQf97mC7zp1c319JrMf 1OzrtOxjE9UD/rmOnf9ebP5D8J+gT3hwS+K/BJ8EfUrwadBnQJ8VfA70ecEXPLgF8UW2HpB8SfBl 0H+DDhd8BXSE4Kugr4G+LvgG6JuCb4G+DfoO6wdw3wV9D/R9wQ9APxQcCdqcE4BYCQ4AnUBwQge3 d3Ei0IkFJwEdCDqp4GSgkzuY9iNTgE4JOpXg1KCDBKfxYNpvTQs6neD0oDOAzijYnLPVBnAmwZlB ZwGd1cG0X/o06GyCnwGdHbQ5h7CVi3OCDhacC7Q557Il4DyC84LO58G0/5dfcAHQzzq4OXFB0IVA FxZcBHRRwcVAFwddQnBJ0KVAPye4NOjnBZcBXRZ0OcHlQVcQXBF0JdCVBVcBXRV0NcHVQb8g+EXQ NUDXFFwLdG3BL4GuA7qu4HqgXwb9iuD6oBsIfhX0ax5Mj6M3FNwI9OuCG4Nuwv5+yW8Ibgr6TdDN BDcH3UJwS9CtQLcW3AZ0W8HtQLcH3UFwR9CdBHcG3QV0V8HdQHcH3UNwT9C9BPcG3Qd0X8H9QPcX PMCj+XERc3zlTXMeZ4B93hS9p3B+cg/gR72Hsf9rhX6T5QEx/TjvYWw94j2MR/jWP3Tdaszbaphv vWfWlY0D4tvK7xYubTXSty6Ii221j7XVvljaao+vrQ7E4bYy1z03YtdBO7WVud7atJU5Jz6utlUX 1lZdYmmrTr626haH22o1a6vVsbTVt762WhuH2yphQPS2MnZqK3PszLSVOUYVV9uqfkDMPoNTW70c 8E+f4VHa6n9rzIp/6+v/W7mUyRfTnFCsH2T6zGnJzzL64uxm/4fZp2DZ5y6bbTNzTrkZiyYq76qc rdrolzNV/e9h/qy6LA8jfV/1zb56nWXmsyWNz4EnKgf2ecyBnb4cOOyQA/s850Cp+Bx4AnPA9FO9 5IC575HJAXOtJ88B/3vIOVAiPgeewBzo4iEHGvquJTc50N0hB/zvoYQcKBa//J+45b/a4/Jf4Vv+ 3zks/9Uel3+J+OX/xC1/s53kZflH+pZ/koCYy9//HtLyLxW//J+45V/f4/I3x6A7+7YH+fKv73H5 lwaW//+H7ezaVvTxPmpbzscxalr2cYw6vnMn4uI+Cd5WVXzmbVXJdz5MXG8rep+yKj47tZW5FqiO 75qbuNpWQ1hbDYmlrd7xtdV7cbitsrO2yh5LW2XztVXOONxW9F4mVXx2aqswX23fYMXdtmrO2qp5 LG3lXw+2tOL3Nz/q6/M7PO9l/O7hCezp8Y7fHRhkxtxudnSIOqcn8zgtcL01WT9uL15M1UqSx+qe aGJIcMZkI498l98K1c9tqJ4ryPyd18ODrQp6GqRfOyd3mBWo4xZ1AoOm3bbH7a7fJo8Vop8rE9C3 n4nNV6h2pYsHB5pH+2tiSHJfW/jnaeYfFm6P33394yIxxu/eGx5z/O4r4e7jd6d3GL/b7Dt71PG7 /6+2B0r7+l1u2wPm2oh8vvPAy/rOP6XbA/73SOCyPdAw6rMV+c8+oYQO2waPmsf+r/9GHjcJH6JO 6ck8mjwKDY+Rx6N4Hq+MCLbu6/zoF27n8fYr0fPYtKvJm5xRd+jSOaNfH1khY5B5rn5EzDz2z9PM PyTCzuOw6THzODQiZh4vi3DP44MRT8Y49PE1Fs/NK5eGqJDLQ5R5NLmR/3KM3BwdW41Ncdm5xpqc iLoXoJ5BkM5bM22rv2XgXj051Vj/PGmNbTIzvsbyGmu217zUWHPPjbK+a/Z5jTXv4aXGlviX1dhR F4ao9BeHKPNo8mjDhRh5PCa2GjvvwuOpsf550hqbY3Z8jY3rNbbCzBC1XU/m0eRGP+PouTk2thrb RL/2cdRY/zxpjQ37LL7G8ho7xGON7eersWMcauwQjzW21L+sxh6cHqJazQhR5tHkUYoZMfJ4XGw1 9sr0kMdSY/3zpDV2+Lz4GhvXa2y3qSHqtp7Mo8mNeVNj5Ob42GrsqKmPp8b650lrbI4F8TWW19js Hmtsel+Nfdahxmb3WGNL/8tq7LR5ISp0is7heXYeV5gSI48nxFZjc0x5PDXWP09aY88tjK+xcb3G FpsbosL0ZB5NbnSaGyM3P4ytxtad+3hqrH+etMYOXxJfY3mNNceVvNRYc+96U2N3WDFrrHkPLzW2 zL+sxm6fHaIaztF5NNvOY2tOjDwOja3Gnpr9eGqsf560xtZdGl9j43qNbTUrRF3Sk3k0uTFtVozc nBhbjQ2Z9XhqrH+etMaeWx5fY3mNbe6xxr7qq7GdHGpscw81trhwzOv/+3kA9LqzcQExXduKfr4c t9O17TV90wTh2na0Rlxm66+wgMdfI8YtClGZFoco82j+RzcvilEjJvEa0U+vE8L0/96Xi+waMYqt v1L41l/mfziIrF9MfgWR9VdiX1v45xm1jeJbf6VYFbNG1HdYf/US1l+T49dfT8x1HsFCjTNja121 /rmHdx4r5nUe5j0yu9S4oTquZrXX9bGP/t7D6qv/60zUzipgFdKftrGOu+lnO+nn2+iov3YB/Tup 9JT8n8/2n9g8JmbPJfa1nZnS+J5PxH7ua5do7xGfX//d/CrjYR1qxnvM6zvXsrxDfpXxsA6tbr1g 1fDlTCrfPB5H2/jXN+MD7Ht2cT/edWjkI61DW7LzpCW3EtwadBvBbUG3A91ecAfQHQV3At0ZdBfB XUF3A91dcA/QPQX3At0bdB/BfUH3E9wf9ADQAwUPAv0W6MGC3wYdIvgd0O+CHiJ4KOj3BL8Pehjo 4YJHgP5A8EjQo0CPFjwG9FjQ4wSPBz1B8IegQ0FPFDwJ9EeCJ4OeAvpjwVNBTwM9XfAM0J8Ingl6 FuhPBc8GPUfwZ6Dngv5c8DzQ80F/IXgB6C8FLwS9CPRiwUtAfyX4a9BLQS8TvBz0CtDfCF4J+lvB q0CvBr1G8FrQ3wleBzoM9PeC14P+QfAG0BtBbxL8I+jNoLcI3gp6m+DtoHeA3il4F+jdgn8C/TPo PYL3gt4Her/gA6APCv4F9CHQhwUfAf2r4KOgfwP9u+BjoI+D/kPwn6BPCP4L9EnQpwSf9uAqxGcE nwV9DvR5wRdAXwR9SfBl0H8LDgd9BXSE4Kugrwm+7sGViW+Avin4Fujbgu+Avgv6nuD7oB9Y9vhP Xv1QcCRoc0DKzQp0gAdXJE4gOCHoRIITg07i4AouDhScFHQyDy5PnFxwCtApBadS9nhrXp0adJCD yxKnAZ1WcDplj0fn1elBZ1D2+HixOSNoc2/W0oAzCc6s7PEAvTqLg0sRZwVtxkgoCTibg0uwsRgk FyfOLjiHg4u5OKeDi7o42MFFiHN5cGHi3B5ciDiPgwsS5/XgZ4nzObgAcX4H53dxAQfnc7G53iiv iwsqe3xWN+cmLuTgXMSFHRzs4iLKHr/WzTmIiyp7/NzYXEzZ4/G6ORtxcWWPBxybSyh7fGE3ZyEu qezxjd2cibiUssdXjs3PKXu8ZuoMzOmJSzs4HXNa4ucdnIa4jLLHy6ZOzZyKuKyDUxKXU/b44NTJ mZMRl1f2eOZuDiSuoOx7tFInJq6o7PHbqRMyJyCupOwxM6gVcWVln7REHami+yG9p5yOHzDfZ75H XFXHd5nvEFfT8W3mW8w3iavr+AbzdeZrxC/o+CpzBPGLOg5n/pv5MnENHV9ivkhcU8cXmM8xnyWu peMzzKeZTxLXVva9IKlPEL+kot9b0vg48zHiOsoeh436KHFdHf/KfIT5EHE9Zd/zhPoA837il3W8 j3kP8Ss6/pl5N/Mu4vo63sG8nXkrcQMdb2H+kfhVHW9i3sD8A/FrOv6eOYy4obLvwU29lnk1cSNl jw9EvZJ5BbE5P3M581Lixjr+inkJ8yLiJjr+knkB8Rs6ns/8OfNc4qY6nsP8KfNM4jd1/AnzdOJm Op7KPIV5MnFzHU9iDmWeQNxCx+OZxxK31PFo5pHMI4hb6XgY8/vErXU8lPld5hDiNuZ+7syDmAcS t9Vxf+a+xO103Ju5J3N3YjOuQFfmLsQdlD0WGHUH5nbEHZX9N1O3Ym5BbN67GXNT4s7KzkHqxsyN VPTxzF5jbsD8CrH57PWY6xCb8c9qM9dkfpHYtO0LzNWIeyh7HUtdibkCsVl25ZjLMJcmNtfOlGIu SWxyozhzUebCxH2U3QenLkBsci8fc17m3MTmXi/BzDmYnyE2uf40c1biAcreJqZ+ijkDsflfSsec htj87wUxp2JOQfyWsvcBUSdlTkJs/tcTMScgflvZ++ioLeaH5JosU0vuM99jvkNszvu/xXyT2NSq 68xXmSOIzf15wpkvE5taeIn5AvN5YnPv57PMp5lPEZva+xfzCWJTq/9gPs78O/FwZR+Do/6V2KwL jjAfYv6F+ANlHyOl3s+8l9ise/Yw/0Q8StnHqKl3Me8gNuu27cxbmbcQmyuuNzNvIjbrzo3MG5jp fZnHKfscDuowYrNuXse8lnkNsVm3r2ZexbyS+ENln+NDvYLY9B2WMy9jXko8UdnnTFEvITZ9k8XM i5gXEn+koo81b7yA+Qti0xeazzyP2PSdPmeey/wZ8cfKPkeQejbzp8SmrzaLeSbxNGWfQ0k9g3k6 sekLTmOeSjxD2eeYUk9xselrTmb+iHkSsemrTmQOJZ7l4A+ZJxCbvvB45nHEsx08lnkM8RwHj2Ye RfyZss8Bj82mL/8B8wgXm22B4czDXDxP2efUx2azrfEe81AXf6HsawRis9mWeZf5HRebbaEQwW8T L3TwYOJFDn7LxYuVfU1IbDbbcgMFDyD+yoP7E3/t4H7ESx3c18XLHNyHeLmDe7t4hYN7ufgbB/ck XunBPYi/9eDuxKsEr3ZwNxevcXBX4rWgzb6KLoDXObgzcRhosy+lk4vXgzb7ajoC3iB4o7KvSfTq TaDNvqj2Lt4MeouD2xFvBb0NtNkX19bFO0DvFLzLwW1cvBv0T4J/9uDWxHtA7xW8D/R+wQcc3MrF B0H/IvgQ6MOCj4A2+8JbAj4q+DfQv4M+Jvi4z/yeLM19kzmWYMbp8l/Hzn8vNv8h+E/QJxzcwsV/ CT4J+pTg06DPgD4r+Bzo84IvgL4I+pLgy6D/Bh0u+IqDm7s4QvBV0NdAXxd8A/RNwbdA3wZ9R/Bd 0PdA3xf8APRDwZGgzTF7xEpwAOgEghOCTgQ6seAkoANBJxWcDHRywSlApwSdSnBq0EGC04BOCzqd 4PSgM4DOKPgp0JkEZwadBXRWwU+Dzib4GdDZQecQnBN0sOBcoHODziM4L+h8oPMLLgD6WcEFQRcC XVhwEdBFBRcDXRx0CcElQZcC/Zzg0qCfF1wGdFnQ5QSXB11BcEXQlUBXFlwFdFXQ1QRXB/2C4BdB 1wBdU3At0LUFvwS6Dui6guuBfhn0K4Lrg24g+FXQr4FuKLgR6NcFNwbdBPQbgpuCfhN0M8HNQbcQ 3BJ0K9CtBbcB3VZwO9DtQXcQ3BF0J8GdQXcB3VVwN9DdQfcQ3BN0L8G9QfcB3VdwP9D9BQ/waH5c xBxfMWPcDwqwj4N5uVd9Kt89gS3/vgU9/Q9T5bINMPoAAP== This is a very surprising and disappointing graph. Apparently the pbehrens() function has some serious numeric stability issues. With other sets of parameters the extremely sharp discontinuities are largely absent, but CDFs like this one seem to be relatively common. Unfortunately I did not learn of the limitations of the pbehrens() function from this relatively simple graph, but by observing an unusually high amount of perfectly zero p-values (and a few other kinds of artifacts you will see later) generated by the Behrens method during simulations. These series of graphs where largely developed in order to try and understand why the Behrens p-values seemed to be unreliable.H4sIAAAAAAACC+3dC5xN1R4H8L03MpXcIaSUmIgeaqi80+iFGIYS1y0hyqvuhNJ155Z7m8rNoxGV ilK4qVRChClSIuMxJEMpKa+eY6SHUnPX/+x18tv/s85ae/lw79Sc+XyWs75njrPnrP3f/73X45zj Oo4zUpR6oiSLMs5znBGiRH9WpzvOaFFqXZF+peO4Tu4TjvNwkuOUEb87TpTB0QeWc5yl4s4hruNU dZ3AT8aMck5S87JOG2eI09vJdPo7rcW/mZHf1RWlgijiKUdG6+Wgzu/vIm4zXfpLHGdvcXExbifH 365bXvzTWmxrgNjaYOdwf+pH/r2qWu3KVcUztynvLs0sSnGafHTxcKpTE01aXDfymGvFfdBkTt15 jnOwMMUZ0bagxzhRWlb6oAe1V9K+FOeHngU9kvemRB6X1bWgx375WirJUlmUkyO/Db62XH8D7nXi /zavs2/4rOSzIm1XfVD9yJ6j20zxu8Vn7BteIfLQ2pVPdma7OeK+juI+eh3Rdq0aaSk38v/mid+3 3l00PPo66fc9ROl7BzX9of3jQv0Ezf453MeHvb+9uE0TJdW3U0tuy5Xx206WsaK9rvViHe95m8s6 xfQNojQVxZO3DtzSltw4ERN9Pvp/VQ69dqeFvz2nhvwb6fk7iSdpHNK9DO5t6T4G32jpvpbuZ/BN lr7Z4P6WHmDpgQYPsvRgS99i8K2W/qvBmZa+zdJDDB5q6WEG327pOyw93OA7Lf03S48w+O+WzjL4 H4dh+mkp8yTl9+qiXC9z992idHaDubs+5No/8rniX/LxjcHYdtz3WDrb4HstfZ/B91t6lKX/bfAD lh5t6TEGj7X0OIMftHSOpccb/JClJxg80dIPW/oRgx+19CRLP2bw45Z+wuDJlp5i6ScNfsrSUw1+ 2tLPKJyh8TSDp1t6hqX/Y/Czlp5p8HOWft7SLyjcDDxLlCbMFzFfAH5RlIbM54FfEuVc5rOZ64Nf FuVM5jrMKeDZdB3BXBP8iiinMp/CXB08R5RqzFWYTwTPpXEC5j+B59F1BPPxzMeCXxWlPHM58HxR yjJ7zA54gSi/OkEfZP4Z/JooB5h/AC8U5Tvm/cz7wItoXIi5ELxYlK+Zv2T+Apwryh7m3cw7wa+L soP5U/AbonzCvI35I/ASUbYyfwBeKsoW5gLmTeA3RXmf+T3mDeBlouQzrwO/Jcpa5tXMeeC3RVnF vJJ5BXi5KO8wLwe/I7eBXsb8JniFbBP0EvBKuc/QucyLwe/KGEMvZH4NvEoeA+j54Dx5DKLnMc8F r5Y5Av0KeI3MUeiXmV8Cr5U5FT2L+QXwOpnz0c+B8+U5R+dnwevlOQ89g3k6eIPC08DvyXM8+mmN N8prDvRT4PcVfpJ5CniTwpM1LpDXcPG8WV4D6vwYeIvCk8AfKPyoxh/Ka+aw3iqvweP5I4Unavyx whM03mbwJ7KPEtbbDf5U9pHC+jNL7zB4ZwjngHcZvFvh8RrvsfTnBn9haTqXt3bD+ysaI9L46xC+ BPyNwXQt0srCdC1zsYWLFG4J3hfCLcDfGkzXYs0t/B27/jf5expP0/gHhZto/KPCjcEHQhj7Iz+F cCPwzwYfZP0Xlc8B/6LwRRrTtfmFGhdbmq79L9DYVbiRxtS3aGjhMqKeqjH1Xc63MPV9ztP4GFFv YDDur/IhjPsvSWHsv1Lf7QyDsb96nMK1Naa+Yi2NK4j66QZjf/gEhU8DV1S4usbU1z2J+ScnaOxf JhtcKYSx/1rZ4BMtTX39Xyxc1eBqlj7J0tUNPtnSpxhcw9KnKnxQ49MMrhnCGC+nG1wrhDGea1ua jvUDGlOu2GDhOpau6wbHE7jPtHQ9g+tb+iyFN2p8tsHnhPBn4HMVxvGmBgp/rjGdm/YYjONV5yu8 C5yq8E6N6Vy8Q+NG7PWqjONjFyi8XWO6FvlEY7r22WZhutb72GAcn2uiMI7XNVX4Q42bKYzjfc1D GMcDWyi8WeOWBlPfosDC1JfZpPElCq/XmPpe+Qbj41sbfGkIY367zNKXs3zDfYXCGzW+UmEcz22j 8CaN2ypcoHE7Fg/cV7F4UxnjtT2Ld+4O7PjpwI437nR2vKaz4zud5YeOCmN+6cTyUSeWv7gzWP7L YPkyg+XXziwfd2b5uwvL913Y+YGM8xdXu/4YBhrnO65x/TEJdCEzzp90df0xBPS3zDgfc60bnK8h fw/u5gbnd7qx65Nu7HqmO7s+6s6u7/7sBuebyMXMLvQXerjB+StyWeYk8F/c4HwZGefTrnP9Pg+6 IjPOz13vBufvyJWZcf6vp1xPjcb+zw2sf0Q+hRnnI3ux/lYv1n/rzfqDvVn/kYzzo33c4PwpuR7z Wbh2lPVvb2T9576sv92X9ef7svGCfm5wPIKM4x03ucHxHnIzZhzPutkNjp+RWzHj+F9/1z9HoC/H taKun6PRbZnb4dpR18+B6HTmwNpR188Z6KtxrajrH6Poa5m749pR1z8G0NfhWlHXj0F0L+beuHbU 9fcxuh/zzbh21PXbBD0Q14q6/t+MvpU5E9eOuv596KG4VlTUb2ceznwnrh0V9RHMWcz/wLWjon43 8z9xraio/4s5m/k+XDsq6vcz/xvXior6A8xjmMfiWlFRf5A5h/khXDsq6hOYH8a1oqL+CPPjzJNx 7aioT2F+inkqrhUV9aeZp4HvEvXpzDOYnwXTvpnJ/Bx4pKg/z/wC84tg2rcvMb/MPBvXb4r6K8xz cL2mqM9lnsf8Kq7fFPX5zAtwvaaov8a8kHkRrt8U9cUG5+L6TVF/nfkNXK+p8BLmpbh+U9TfNHgZ rt8U9bc0Hi3qbzMv15iOnXc0pmNphcErcf1mCL+L6zcVXoXrNUM4D9dvGkzH+moLT1B4jcYTDX5Y 4bUaP8IerzK276MGT2L7z+THWDxwPx7CGG9PKPy2xpMVxnifEsJ4/DypMB5vTym8VOOp7Pg2+WmW H7ifYflFZcxH0xRerPF0lv+4Z7B8qTLm1/8ojPn4WYXnazyT5XuV8fzwnML4ep9XeJXGLxg8K4Qx 37xo6ZcMftnSsw1+heU3k+dYei67PuGex65nTH5V4Wkazzd4gcLPaPyawQtDGK/vFll6scG5ln7d 4DcsvcTSSw1+09LLWHub/JbBbys8TePlBr+j8HRm7P+sYP0jlbG/tVLhkeB3Fb5bY8ptd2mcx/qD KmP/cbXCf9eYrnWGMWP/dq3CQzRep/BtGuez/jb3etfv44f1Btaf537P9cckwnojGy9QeRD4fYM3 sfEIkwsM3szGO1TG/bdF4SEaf8BeL/eHCg/SeKvC/TX+SGEc7/k4hG8CbzP4Eza+ZPJ21x9TDOtP 2XgW92cK99F4h8I4frbT0rvYeJzJu11/jDie9yjcU+PPDf7C9ce4w/pLUT/BC++vDP7a0t+EcEVw ocF7FT5B4yKD91n6W0vT55NU0Pg7S39P8yca/xDCx4F/DOFjwQcM/onmfyz8s3B5g48BH1S4HPgX hctq/KtwGY2Lab7LYBdMb0jndpjp//D36o+U752n5072Dr2P/bd1nvL/oX/FdZ2e/9p0PojrPD2/ bdE/4bpOhQ8w/4jrPD0/ttDfa0z78Dvm/biu0/OPJfQ+5iJc5+n5xz66kPkbXOfp+bkK/RWu6/T8 3Ij+gvlzXOfp+bkcvRvXdXr+uQO9k3kHrvP0/HMd+lPm7bjO0/PP5eiPcZ2n5187oLcyfwimGNzC vBlcyfOvxdCbmDeCK3v+tSV6A3M++ETPv1ZG47hlFS84DkDOY8Zx36pecJySvIIZxw2recFxQTKO 653kBcfxyEuYcdytuhccRyPjuNjJXnAcjLyAGcexTvGC41Lkucw4L1LDC86jkHGe5VTPH1tCP8+M 8zqnecF5IDKOu9T0gv1Q8jPMOC91uuePlaInM+M8WC3PHytGPwqu7QXn1cgTmMeDU7zgPB4Z5/nO 8Py5DfQDzKPAdbxgP5qczYzzlnW9YL+ZjP3gM71gv5Y8ghnnWet5/twnehgz9nPqe8F+Jxn7gWd5 wX4LeQAz9jvO9oL9BHJH8DmWPtfSDQw+z9LnG5xq6YaWbmTwBSGM6x4utPRFBje2dBODm1q6maWb G9zC0i0NvtjSrSx9icFplm5t6UsNvszSlxt8haWvtHQbg9taup3BV1m6vaU7GJxu6Y6W7mRwhqU7 G9zF0leH8Gwvtt9GfTBaQ9vV80tp/Iy17rJtGoOx7Uz+s8E9LP0XS19n8PWW7mnwDZbuZeneBvex 9I0G97V0P0vfZPDNlu5v8ABLD7T0IIMHW/oWS99q8F8tnWnwbZYeYumhBg+z9O0G3xHS/FxB+ZrW It95lM4V0Z851Pf3Yl0SzhX0eZddveB5vavivHqPPOfSebpboq1+c09NW90vzwWlsa3Ws7ZaH6et 1sm2eq8Ut1VNN9hWZFVb0fteqK3oPdWlta0GsrYaGKet+su2GlyK22oBa6sFcdrqVdlWC0txW5X1 gm1FVrUVzdtRW9H8WGltqwwv9ppB1VYdvUPXDIfTVv+r7+r4vT7+aMVSdVnHmHDZdRBdM1eG31WT 9dPpPbc0pkDvTZJ9M/pMcfoOnkjcpe1u3fX9Xa2jz0F/VgcWh8XyJ4PmCUSU0Ws7NhEDJSoG1oeM gVUyBgoUMbA+dAxcmIiBEhgDNd1wMUDv76YYoPdZ8xiIPoc5BholYqAExsDAEDFwjXwf+wA5h81j IPocriEGUhP7v8Tt/wUh9/8cuf8XKfb/gpD7v1Fi/5e4/U/9pDD7v1ju//Je7P6PPodp/1+Y2P8l bv9nhNz/NP89QPYH+f7PCLn/G1vs/z9CP7udXLfZGEzfp8T72W0cv4/VXq7LLI1jEryt0qR5W7WS a2tLe1vhZ3akSavaitaktpfn79LaVp1YW3WK01bpsq06l+K2ws9iS5NWtdVXMl/tdUpvW41lbTU2 TltFc/uDTmIM9XAfX19xf5jv4s4u45cj+13cScn0/dlZD2S7SaOzXbqdlPSGM0/crmyY6rYtX9e5 pdz4rLRqx121eVF9J0fct/SyM5Lp79xfmOK0FGWSeOzUOrlOkqj3bJ+UPOlH/zu4M/rUdbLEfU29 ocOoTj85wq2+3Dicbv2f8VnHy7aIbpO2n1vofxd309UNYr6LO78w9ru49xbqv4u7iuK7uGk86HC/ i/v/dY3bWF5L6K5xKRbqyX5OM/n+A7zGjT5HOc01bvfIOFeqc54ojeRrpOvdsvL22CMU09GfoxHT VUaJuBSFbimmOoyKien2PKbnFaU4B0WspI7yY3rl3mBMUxtTDNWOvMNDxI94fHHLasl0X0ZRbExH t0nbzyryY7rCutiYzimKjenZRfqY3lhUMr5fPpFv7WNz1r3ZbtP7sl26pdjYcW9MbHaIl29X3qvO txQTkc/ZExtIFnFLZUXG8uH5oqjybXSbmG9nrk/kW55vqT8SJt8+KfPtMjc239JzhM23DX+n+Xbz Q9lu/j3ZLt1STCVPiInp9Hj5dv9DRybfRreJ+TZrYyLflvZ8m5mT7R4UhW4pNmbmxMRmx3j5dkzO kcm30W1ivq1ekMi3PN92MuTbvjLfpsl8e4Mi39JzlNXk22sir42ybervLs8mjct2J4pCtxRLaeNi YrlTvDxbZ9yRybPRbWKe3bElkWdLe56dOjrbPXeMiLHRfmxuHh0Tmxnx8mzu6COTZ6PbxDw7cmsi z/I8S+OhYfIsfccH5dlfndg8+40TNs82/N3l2R3rariZ+TVcuqVYOlXUWSx3jpdnHfHYI5Fno9vE PNthWyLPlvrx2jU13KS1NVy6jYzXromJzS5xx2vX1DgieTa6Tcyze7Yn8izPs2ND5tm7ZJ6dosiz Y0Pn2UbaPPtHn8fC9wKM8WLdzgmuYeBWvd+wjSzjDO83tM0TX7NzWK53FMbA88SxLgrdRsbA82Ly xNU8TwwT54VcGgPP8/PEKHYOqyDPYXQcJ8M5huIrGc5hx0THwPMO5YmW8hyWvCs2T2QozmGZhnPY xMQ5rMSsvU0x5LmZcp129LPV6zqxa2/pOf6kyXN0PFzq9HP6i+Ojn3OrM1S8wgaidBMaLNRf/L6i KMcfeh2/1Y+XbXKMvK0E90Ufk4iRoxsjTQ0x0svxv0PrTMf/LO8Wihih5yhjOBde5lzuXCljoaJi 32KurijPK478O6n+X7jyV/q8mwAA This graph of the difference between the two distributions is continues on certain intervals, and in other intervals discontinuous jumps are more prevalent. These discontinuities will line up with the previous CDF graph of both distributions.Precision and Run Time of Patil ApproximationFrom the previous CDF graphs of the Behrens distribution, numeric stability problems exist in the R code for calculating statistics of the Behrens distribution. I did get the latest copy of the code from Peter M. Lee’s website.http://www-users.york.ac.uk/~pml1/bayes/rprogs/hdr.txtLooking into the code it seems that some of the functions are performing numeric integration in multiple dimensions. More details are provided in the following table.FunctionComplexityRun time (in seconds) AMD Athlon XP 2200+gbehrensLineardbehrensOne dimensional numeric integration of gbehrens()0.005pbehrensTwo dimensional numeric integration of gbehrens()0.07qbehrensRepeated calls to pbehrens() based on a “precision” parameter, non-deterministic.2.5rbehrensOne call to Qbehrens for each random number.2.5hbehrensTwo calls to qbehrens, does not assume symmetric distribution.5There is also a limited table for the Behrens distribution in the back of Lee’s book and in the book when the Patil approximation is explained, he states that the provided table in appendix B where calculated using the Patil approximation. Observing the differences commonly in the few hundredths of quantile, it seems calculations based on quantiles like calculating confidence intervals could be questionable. I presume, due to the numeric integration involved, that more precision can be had from the provided R code, but this in turn would have a prohibitive effect on the run time needed for a simulation.Table provides several different degrees of freedom for the first and second sample, but in this table I just choose df1 = 6 and df2 = 12.Theta (degrees)AlphaQuantileQbehrens(1-alpha,df1,df2)Difference00.101.361.37-0.0100.051.781.80-0.0200.0252.182.23-0.05150.101.371.38-0.01150.051.801.83-0.03150.0252.192.29-0.10300.101.401.41-0.01300.051.841.85-0.01300.0252.242.240.00450.101.421.43-0.01450.051.881.880.00450.0252.322.310.01A Note about P-ValuesComplications developed using p-values with the Behrens distribution, and so they have been omitted from the main simulation study. On theoretical grounds, if the distribution that the p-value is taken from does not represent the data, then the p-value is an approximation. Since the distribution of the unequal variance two sample problem does not have a t distribution, p-values generated from a t distribution are suspect. Since the Patil approximation again is not the true Behrens distribution, caution must be exercised.In addressing this possible issue, the simulation has been done using confidence intervals side by side with p-values. While in situations whereH4sIAAAAAAACC7t+9tgsBjA4wKLAxMQJYn2OYGQAMphZGRkYmBhkwLKsQMzJBGMxMTJCWYxM//// B7P0GCWgYtxwdTxMCkwHWISALDU2fgYphv8gxQwCINuArGVA3MDCwHAMaBg3VA0Pg29iSUZIZUEq A0MA2O7fTAr/IS6cALKUgYWJQSAkMze1WMEvtVwhKD83MY9hx5LP5QeBWMHga/lhzrQTQEMZdIGq OYC0EdcDRn4WkFajShhfEOx+w0qI+Q3/YOaDPAwyP7gyNyk/h4GhgZOr3+GjEA7zGRlA9Ae4PQ2M qswgc3MrYXwHBggf3R5QEDIg2dMsyHUJtz0MUHsY4fa8B7vftpILGmpc4JAFBw80zAQY2MG8PeC4 YGRiUgquLC5JzWU4ATKXAahDkaELrAFExHwWYkD3EzNYPwDu8YQ9IAIAAA== , theory demands that the average number of p-values less then 0.05 is exactly 5%, but this does not hold whenH4sIAAAAAAACC7t+9tgsBjA4wKLAxMQJYn2OYGQAMphZGRkYmBhkwLKsQMzJBGMxMTJCWYxM//// B7P0GCWgYtxwdTxMCkwHWISALDU2fgYphv8gxQwCINuArGVA3MDCwHAMaBg3VA0Pg29iSUZIZUEq A0MA2O7fTAr/IS6cALKUgYWJQSAkMze1WMEvtVwhKD83MY9hx5LP5QeBWMHga/k9zrQ+oKEMukDV HEDaiOsBoygLSKtRJYwvCHa/YSXE/IZ/MPNBHgaZH1yZm5Sfw8DwUYjLacFHIRzmMzKA6A9wexoY tZlB5uZWwvgODBA+uj2gIGRAskeFm+s5bnsYoPYwwu15D3b/zkouaKhxgUMWHDzQMBNgYAfz9oDj gpGJSSm4srgkNZehD2QuA1CHIkMXWAOI2PNZiAHdT8xg/QBzL4SwIAIAAA== . In these situations whereH4sIAAAAAAACC7t+9tgsBjA4wKLAxMQJYn2OYGQAMphZGRkYmBhkwLKsQMzJBGMxMTJCWYxM//// B7P0GCWgYtxwdTxMCkwHWISALDU2fgYphv8gxQwCINuArGVA3MDCwHAMaBg3VA0Pg29iSUZIZUEq A0MA2O7fTAr/IS6cALKUgYWJQSAkMze1WMEvtVwhKD83MY9hx5LP5QeBWMHga/lMwbQ3QEMZdIGq OYC0EdcDRlEWkFajShhfEOx+w0qI+Q3/YOaDPAwyP7gyNyk/h4FBhZtLa8FHIRzmMzKA6A9wexoY tZlB5uZWwvgODBA+uj2gIGRAsmeqIBc/bnsYoPYwwu15D3b/zkouaKhxgUMWHDzQMBNgYAfz9oDj gpGJSSm4srgkNZfhDchcBqAORYYusAYQseezEAO6n5jB+gEONWGMIAIAAA== , the observed significance level is calculated as the probability that the true difference in means is contained within the calculated confidence interval.SimulationsThree sets of simulations where performed. The first simulation compared the Welsh T Test as implemented in R as t.test() with the Behrens distribution approach under equal means, while varying the sample sizes and standard deviations.Equal MeansThis simulation was performed over these values. n.x=c(3,4,5,9,15,20,30,40,75,100) mu.x=c(0) sg.x=c(1) n.y=c(3,4,5,9,15,20,30,40,75,100) mu.y=c(0) sg.y=c(seq(.1,1,by=0.1),2:5)Each combination of parameters received 4 simulation iterations for a total of 5600 iterations.H4sIAAAAAAACC+1cDWwURRR+s1C8WjSHAVJ/EqG2iiaaKggVK3JBESLUiwJuTsSiJSk/arXYFtNo EzEi/qSaapCgLYpYrWA1GLAWFVNjBYKNFjFGExONmvjTllRFpZ7v7c7YvZnZu6Ue8cruJa9vZnZ2 Zve7732d2Z0bBgB1aCPQzqS0AdCKJj775wM8gjbh6vmzARiU3wKQN9KufzLaKlExC+A9LLybAYxj kPCJvpgFoekj4Rq4G5ZCBZRDBP9WWMcK0EajhbBrkc5ypOXy69FXMLoSgN54PO7sp97ul52EfyLY 13LsbRUM9TPJ+ntf7sRvx2HLi4Cxir48mPbVFdWUJog2vF1g1VmEZQ7IoGAHwNGePLh3zqHY42jF Y76IEV6hw3nw+5JDsXBvnlWvduGhWD+/lzHcTkM73TqaeG/tdgdsMZ47Pf9w9avh8y3sclfSdYYt X4HH3j7ncPVoq+rEb0+HVlaPZSVYRvchcB1nIcWs83bg8cj3fdXiPul4DK2siqAf/H6YI31Kku9n qPXl8kmadpJx4ee4Hq/0cCEUpu9v3qcmW/eJychvCL0DRzDdeXEhm3NSAdye9URtTe7J/T98PBnq sey9WeeE6TpXI2faEeOxeE5Tfjusw/SSa0PhDUdsDkRvLYCjWFZkVK6mNH3CeM6MH7urydufJ2pH cSxEn9R/cZ/NhV2nqVyI9qlcIP4m40JDX2ZwIVPqX4t+JlqhnYcJ/FwbrcHPG8i11w0179ZuLk/L mJ7J212BmQu5Fohj43n6bLQFaE1o+cw+5zVmX6MlfzO/jyw8+F1EtHEq8VZic5x/yjF9IyzDuKhE TZ6AinwhVFlxcg+WVlp6lMPvPWfw+i0/ipflOMpE3ontscbx8dV0O45/OmiyUjTyFEc7Dipx/Ksc x/0Yo8VoXQftOA5JcUzxOqe00kqPwruqwVgi7aXy+l41jkWf1H871/S68Wocd2k0vTeFpo8N4jhj 4ni7kTyO69GK8UAj1nua2WMvOY6pjZwkcVyG6avhLoxaio0JMB+jdyncAZU8HrPta7c88X+kjZeV F8dCJxgXhqo7a0fYdjx0p/AjHD90moy8NX7oVHTnN1l3ujHWz6Lxw0e27vzQk6g7xDTi2v3YAekC WQXXnQqN7og+qf9NXHeOnKHqTqtGd7pS6E6/Zixp/gfd+b/iluL1OpY8btfyWDqf5jvo72GJcSva yE4St6WYno3cWmbF7jKM2NtgDZ9XZTniM3uIsXq88JvO03SdOB2EIjSDe3B46om5RIRoj84bO3gv cDm/P/FdUPsLsdJUnq8y7Hwxr0f3R9/nzWg3YHkN2o3StU9y9OUnrCi/JAlWS9GX+hSrvRJWe12w 6uRY7fcxVpeyRKwor8NqMrOxmsb8i1WThFWTC1bPcaye9zFWOUYiVpTXYZVt2FidYvgXqypD/T+o w2q1Mfh/MBlWmTgvD+032VX7TEbempfvU8bHv8vj4x0416XnZ1377PFxpzQvr+NjYHoOl/tLfW0F tkNjL2ov6ni+liPm5fsGx8e1/Pla7rnq+Lhe83ytNcXzte5gXu6LeT9pQU2KeX8p98ux3nL090rz ftHGiCTzhwXWvV1k3V82n9dnB1zIKC7s9ciFdzkXujVc2HsMXLgk4ELGcoHGzV64cAGzuXAlU7kg 2vDChSkBFzKWC00eufAU58IrGi40HQMXpgZcyFgu5BjeuEADd+LCOEPlgmjDCxeKAi5kLBeqPHJh JedCnYYLVR65cPEQx44nwnx6Ls1bHfPpuXwuJs+nr+HvMOieZ/n02YOM1Uyel7GagXalEWDVyxKx orwOq1+YjdVh5l+sGiWsGl2wepZjtdnHWJVIWJW4YDWPYxX1MVYDkIjVAOix+otrexz8i1WLhFWL C1Yvc6y2+RirmIRVzAUrMWZYPASsgue6mbuG5+gBky1AI0/vCJoPKO8ojihrB3vyoBjt6wN87WCS NTy0Npzsw+gH1V1o9T3qOwrRp7V2sMd+R9E+Q7N2sEezdrAnxdrBE2QNz1Q+Rk02jyI7D+0KrHcZ rcWR5lGiDZZkHhXl95Y9DNa95r9vstI9JiNP3Onao3D3D7f3az/t0b9fO5v/RmIirLeuuAzrx4vH h6lM935N9Ol8v1YTCd6v+V1XOzpMVoRGnrjxaIfCzT/ddLW5Iz26Kvp06urYqwJdlXW1l6V+PkW6 +g2zdfVvpuoqtZH6+VThv9qaPUw0NrTLZOEPTUbe0tidCo//ctXYnWnS2J2qxn45O9BYv2vs1204 dkUjb41d2xRuHnXT2I62NI1d21SNrZkbaKyssY0eNfZJrrHbNBrb6EFjLxmGGrtrt8n6201GnnhU t1vh8YCbxm7anR6NFX06NXbmvEBj/a6x/c0mK0QjT9xY26xw8283jf28OT0aK/p0auyXJYHGyhpb 4lFjI1xjF2s0tsSDxk4ehhrb0IJjWDTyxKPFLQqP424aW9OSHo0VfTo1dtNrc4xAY/2tsau24xh2 m8nIEzembFe4CW4aG92eHo0VfTo1tugNlZt+19gB8KaxvWBrbI5GYwcgtcZOGYYa27rZZPlo5IlH NZsVHjM3jW3YnB6NFX06NRbeDDTW7xq7bgtq7AsmI0/ciG5RuGm4aeyqLenRWNGnU2M37Qw0VtbY Fo8a+xzX2LdA1dgWDxp76TDU2Ekvmaxuq8nIE496tyo8HuGmsaNfSo/Gij6dGlvWFmis78exG03W /AyOYzfa3MzdqHBzpJvGTtmYHo0VfTo1FnYHGitrbMyjxs7nGluu0diYB42dmkJjh4rNXG6PIQ6L DDWfKftXlDnWVzVo8hFpfws5Xwb6/S5uRXv6OK1LHg7YEnYPQuJ+F3LeiWWDJv+gBtsn0R4Ae38M v2JL2K10YBnX5COGO9bifN3eI/TbYMb8i22cc8y594icd2IpYy3Ol7GlZwq099o0H2NL2D3swHKF Jh8x3LEW5+v2gXmIxjc+xpawWw+J+8DIeSeWKzT59Rpsy7F8Hdj7xvgVW8LuZgeWn2nyEcMda3G+ bk+em9B/7mNsCbvHIHFPHjnvxFLGWpwvY9uN5Y+AvYePX7El7O50YBnR5COGO9bifN3+SLfz8Zdf sSWc1kDi/khy3ollRJNfo8GWfs9YDfbvaWd53E/pVH6twNum9D8veJJBaF8AAF== Under equal means, the welsh p-values look uniformly distributed.H4sIAAAAAAACC+1cbWwUxxl+Z7Gdu1xILxAbA7YCBrdOpVYkEOJSh3CFEKMYeqUhvXXhaloageNG B3ZsN3IVfrhKUlx0ad2IHxU9oUSJKhqcih9V47b5kSgI0Ya2TkjT5l+UWEWtbWrJFYJe33d3Jp6b mb073EM9s7vSe/Ox87H73PM+N7M7NwwADqMtQFtOcQtgBE0c57YDHEFb8cD2rQAMer4B0FDhlr8Z rUsUrAR4HTMPMYBqBjlH/MVKCG2ogAfhEOyFFOyHGH6mnHONaLeghbBrEa+U4mr+TgxTjK4EYDKb zcr9pN1+2U34EcO+DmBvXTDXo8n5TNauHK3GlhfVsOWpqQa494P7+ihOEB17rdEp8wjmSZBB42mA KxMN8GTrhfajaC23vd9OeIUuNcBM8kJ7dLLBKTew60L7NL+X27gtQlvqnM29t1G3A7Yb625Yfanv ZPROB7vax+g6o06YwnOvrbrUd4tTdOXoUhhhaczbgXl0HwLXagcp5tQ7jedjH0/1ifuk8+1o+3oJ +tnvh0nxhXm+n7mWV/ObDO3k48I/sma8SsOFUJS+v2P1NoN1NqPwWOi3MITxM3etYa03NcJ3Kp8b OFp787nxt9dCGvNe37wqStfZg5wZRYxfxrKZ1aPwDMaTD4Wix/7tciD+zUa4gnnNVncPxemIYp2N F8f6KHSP5waqOBaiT+q/Zcrlwq8W6VyIT+lcIP7m48LwVHlwoVzKP4ThJrQ1bhpW8LouWrPHL5Fr r1p62qvdWh5XMV3O2+3ExOe4FohzNTx+B9rDaCfp+2ZunV8z9xod+dv0cWzXOx/FRBvUXpvC5iw/ yB++BN9GPT6En49DN95hCmv1Or7yBOZ1w61YJjJ7H5/EIxwTilfxtJwn0jLO1+rT11ffXZ9+YYnN rtTYjELyqa4lmk//XvXpafTXFrRnlrg+HVJ8mny3taPbiVfhXfWjX5EOU356Uvdp0Sf1P8r1fahG 9+nzBn2fLKDvtwc+XTY+/YqV36fTaC144mdY7nnmjsNUn6Y2Inl8eh/GH4CD6L3kGytgO3rxXse3 3Xph7sdhPuarcPFy0uJc6Abjwlx1Z3CBa9dDdzqW2Wxsqc0oJL9vWqbpzh9U3RlDX69D27LM1Z3x iVzdIaYR157CDkgXyN6Kv9l3Hi1l0B3RJ/X/U647Fct13Rkx6M75ArozbRhXJv4H3fl/+S3565dZ fr8d5L50J819MHyC5fqtaCOcx287ML7V+R0+6PzyPg7fgu/yOVal5J/hOfrq9cJvA4/TdeLUEJrR LB6CFFJPzMMjRHtU7/bZe4Ev8vsT3wW1vwsLrefpXstNt/BydH/0fe5B+yrm96N9Tbn2JqkvP2FF 6WQerPaSJvkUq7MKVmc9sDrDsTrnY6zuYblYUdqE1VrmYnUv8y9WGQWrjAdWxzlWJ3yMVcTKxYrS JqzClovVQsu/WPVa+u+gCasea/Z3MB9W5Tgvb6632ck6mzXzZ21Qr42P31bHx6dxrkvP0urq3fHx GWVefpiPgemZXO0/0wMpbIfGXtReXHrWFhHPUupnx8cD/Fnb6k/r4+O04VnbSIFnbWPBvNwX837S gv4C8/4OHh7AcgcwfFKZ94s2FuSZPzzs3NvnnfsL83l9OOBCWXHhbJFc+B3nwpiBC2evgQt3B1wo Wy7QuLkYLnyWuVy4n+lcEG0Uw4V1ARfKlguZIrnwE86Fnxu4kLkGLqwPuFC2XIhYxXGBBu7EhWpL 54JooxguNAdcKFsu9BbJhcc4Fw4buNBbJBfumuPY8UaYT2+jeas0n6Z0EvT59INou9Honjf79NmD itUmnlax2oh2vxVgNcVysaK0CasJ5mL1L+ZfrDIKVhkPrI5zrE74GKu4glXcA6sdHKudPsaKHlbK WGXBjNVVru3Mx1idUrA65YHVLzhWr4J/sUoqWCU9sBJjho45YBU81y3fNTwDUZtNfspmFNI7gi1R 7R3FeW3t4EQDtKB1RPnawTxreGideFRaw5Oe0N9RiD6dtYMT7juKMxsNawcnDGsHJwqsHbxB1vCs 52PUfPMoss+g3YflvkBrcZR5lGiD5ZlHxfm9hefButfmxTZLL7IZhc77tcUad//o+X5tsfn92h38 /xIr4QfOFe/D8tmWmijlGd+vLdbfrw3Ggvdrvl8bWWWz/dU2o9BZG1mlcfNPXrq6pao0uir6lHV1 xZZAV1VdnWKFn0+Rrn7IXF3NMl1XqY3Cz6fWfKKt4fmisWGb9YRQY8Mujz8MaTz+s6fGhkujsaJP WWPHtwYa63eNnY7YrA2NQuJGJqJxc8xLY0cjpdFY0aessYPbAo1VNTZTpMb+mGvsKwaNzRShsXfP Q42tyyZYz38SjEJHYzGu8PgdL40FrFMSjeV9yhrb1hZorN819j1mszVoFBI3Bpmmse96aWyGlUZj RZ+yxo7vCDRW1dh4kRq7mWts0qCx8SI0du081NjhCpuF0CgkHu2u0Hh8wUtj+ytKM44Vfcoa2xRv tQKN9bnGziRYGxqFzjh2Rvv9f89zHDuTKM04diahaewbO3Vu+l1js1Ccxl4CV2MXGjQ2C4U1dt08 1NiRywkWQqOQeNR/WePxX7w0dvhyacaxok9ZY4d2BRrrd4194WqCvXElwSgkbsSvatx830tju66W RmNFn7LGNiUCjVU19lSRGnuCa+xvQNfYU0Vo7D3zUGNfHk+wOjQKiUepcY3Hf/XS2KHx0mis6FPW 2Mn2QGP9rrGHLybY9N8TjELiRutFjZt/89LYfRdLo7GiT1ljh/YEGqtqbLJIjf0K19gug8Ymi9DY 9QU0dq7YbOP2Q8ThEUtPl8v+FS9J66uGDemYsr+Fmn4JzPtdvIj2/HValzwfsCXsjkDufhdqWsZy 2JA+YsD2R2jPgrs/hl+xJey6JSyzhnTM8sZa1DftPXKQr031K7aEXRpy9x5R0zKWKtaivootrfs9 Cu5eJX7FlrB7VsKy05COWd5Yi/qmfWCept9AH2PbyTGQ94FR0zKWnYb00wZs92P+9/n/IPyKLWG3 R8LyXUM6ZnljLeqb9uT5uvMOz7/YEnZPQe6ePGpaxlLFWtRXsR3D/O+Bu4ePX7El7DolLGOGdMzy xlrUN+2PtJ+Pv/yKLeH0KOTuj6SmZSxjhvSjBmzp/4y0v2p/AWzl5wu38msF3jbF/wtx1AGGdF8A AF== Under equal means, the Behrens p-values look uniformly distributed, although the distribution seems to be tilted a little, with a bias for higher p-values.H4sIAAAAAAACC+1cbUwURxieOT48PDXnZ45IEFCsRCQgiB+cuFerYBQlVZRQtdrSelpqTkG4GpL6 wx+mpc2ZWOMP05qm/Wca2vjDRtL4o01tpAlJaTVtJTQt1aStHJSqtej1fXdnZJn9uJMe6eHuJi8z 7+x87Dz7zHMzs7tQQsgxsCSwuWBtDkLawfjRWUXIm2BZ66rWE0LJts2E7EtS8k8Ga+AZUwi5DImH KSGzKRl1VH+YQpyrkkkFOUz2kgDxEx/8DcjncsGmgDnhMng8RRUX05+FMEDxSggJRyIRdTshpV06 Cf74oK390FoDGeuxSP77jid74Wyo+YCL/hAYyCHLb6xuwThCdOZSrpxnO6SpICO5FwgZ7s8hRyuv 1b0N5p3+fR3i5RzMIXd3X6tzh3PkfK011+qGWF+mM5sBli6fHd23DqUBuhPKrlow2HLenSdj53kF r9MthwE4d2n+YMsUOWv2wnTSTkOQthnSsB8c19kyUlQudwHO+24OtPB+4vk6sPpmhH7k/lBVfKrJ /RlrfjF9kU49Zlz4I6KPV3y44HTj/ateKdHPV0gUwzPOz4gHwitFhbRyUi55NeVka8gzedBTsYSE IO3y2vluvM4m4EwHYFwCec8t6CAnIL57o9N95p7CgeoXcskwpK1wNDZhHA83lCn/rbsFQ+U42ZrK sOBtYvveAYULF2douVA9oOUC8teMC6cGEoMLiZJ/I4QSWKHikyxWVkFr5PgEuPaxQ+sb1ethcRHT uazeA+AsYVrAz81h8Xlg2zAOiV2sTJJDuUZZ/qSbvppvf/XxOvCaNwlsjrCjDeJPk5dAjw/D34Ok EXIHoFSzPFaOQFoWeFlkB8Qa4Kxfc76RTIM6XCP9fBR3Mcwwnsp8dRqPp7JwuirNNYKVaXmXcB8f VzPG9/dD0YxwmUQrwTDEMXuxTKMZf4qaMQR64AXrLlM0wyloBmpD5Z5GOZ4KvQrCuEWdx/RQWKsZ vE1sv4P9fvw+R6sZXTq/H+Eovx+zbM1IGM34yGGuGSEwL5x4D/Kdpso8T9QMrMNlohn1EF9HDsHo x7GRRapABfbK2qGUS2M6kMbmlMkKXrLPzzmfMC6MVXeOJyk2HrrTVC7RztUSxRDHfVa5RneGRN3p hrGeAVZbrujOrf7RuoNMQ669Dg2gLqAFmO4EdHSHt4ntn2W6Uz9XqzvtOrrTFUV3hnTmrbX/QXf+ r3GL43ULNR+3x9lYysO1FYRH6Ohxy+tIMxm3eyC+Xv6dPyT/ch8kL5LX2BouRTU+08Y4VscLv1Us jtf5PNgKMAcLiSrElqjBiOD1YblZI30hZax//F5g/TWQqZT5zQ7F97J82D+8n7vAtkJ6EGyHcO2L VG1ZCSv0d5tgtRfCPRbFqk/Aqs8Aq58ZVjctjBXOQdRYoa+HlZ8qWDVQ62IVFrAKG2B1m2E1aGGs uJartV0PqybHiLabYZWIa836IoleL5Qohjjnyi/SzPn+Eud8F2D9hvtPlUXKnO+KsNY8xuZ1uI/l uR1qDUA9OJ/A+qpV+1MuhgVvE9tvZftTtbnaOV9IZ3+qPcr+VLe91rTEWha1IBhlLYtjpQpsP+TD JwlHhbUsryPFZE6M64Ul0LsCUvSoj2lszcrnwDYvEocXfTHy4hvGizs6vOh7LF4UkmU2LybE3lc0 XuC+VR1VeBGkWl7wOpJNeLFN7huyotDmQwLzIRwjH3oZHx7q8CH8WHxYZvMhgfnQ7IiNDy87FD4c d2j5wOuIhQ9FY9SHJ2GdtQHXM6p1Fvp+ol1nVSDeYNjntRZdk4pYScwXsSoHW+OwsbpKR2OFvh5W X1EFq6+pdbGqEbCqMcBqK8Nqh4Wx6iGjseoh+lj9yPSql1gXK7+Ald8AK67tB8aAlb0vk7jPlZNL JBosliiGuMfXWazZY7yjeZ+lP4d4wW4Vs/dZTJ4r47uRaF9Wf9HSBRbq1+4x8jbl91n6lT3GjpU6 77P067zP0h/lfZYn5LlyKZtLmM150Z4CWw35VuLzYWHOy+ugJnPeata3tAnwLtYHpRL1gGGI3Gko 1XD3rtH++IlS/f3xeewd4WzyhnzF9ZA/4p3jxjS9/XHepnp/POi198etrqvteRJ1gmGI3Ajmabh5 z0hXT+XFR1d5m2pdnbXG1lVRV6/S6HsJqKufUkVXb1CtrmId0fYSiuSdxkLNezmJrrOefIm2LQat zVe43LtYw+W/jXR2eHF8dJa3qdbZXp+ts1bX2YsFEs0HwxC5caxAw837Rjp7tiA+OsvbVOts6zO2 zoo6WxOjzq5lOrtPR2drYtDZpRNUZ4fSJeoHw1DmUrqGy/8Y6ez19PjoLG9TrbOVFbbOWl1nT2XA fBYMQ+TGzgwNN4eNdDaYER+d5W2qdfaXDbbOijrbQ2LT2U6i6GyYaHW2h0TX2eIJqrMl8yQayJQo hvJ8NlPD5QeG89nMOM1nM7U6277J1lmr62ztTIm6syWKofydz0wNNx8a6ax3Znx0lrep1tlNW2yd FXXWH6PObmc6e1RHZ/0x6GxJDDo7Vnw2MHsLsNju0PqJ8JwqIjxXX0bNfTF/xOA5/AP2HH45HZ/n 8BMBW8TOKXyfIfrRsHfqYFsM6ansew6rYovY7VI9Xz2n4/tMsObl9b6VeQ7C9y2MLWI3rHon4jsd X43lOR1/WOcdinch7T7YdQtji9jlqLByObS+GksRa15exLYb0rMgfarDutgidktVWPl0fJ8J1ry8 iG0a/s8QhqtVsUWcyoVvwkTfZ4I1Ly9ii3MEL3tf1KrYInaSCqvzOr7PBGteXu/7PMS8zcLYitj9 FMU/b+CL2IpriVi+fZzGrpWwujH+L5vzapRUTgAA The difference between the Behrens distribution and the Welsh t distribution seems to typically calculate higher p-values on average then the Welsh t distribution, and hence the higher delta.H4sIAAAAAAACC+y9ddB2xdGvu3pwCO7B3UKABIK7a5AQ3IM7BHd3d3eHBHcL7u5OcHe308M91P5O //qc2rX/2lXXStV8F/0G8uO9vvd5nnutmem2ruv29DWEr/F8HV667nJfv/3noaW77hBfEy+89CJd Z92Oh4zdjfrK4O8f3tdmv/2NQ3Xd7f6L21jXjWnd/+s/y543VDfsHEN2i3bbdOt0W3UbdfP7/93q 1/9uCl+/8zWs/2v89tdD/Y+/jr++vHMrq/8mXffpL7/88j9zjhzk2jD+f+b3rI09bbPu//Q/U3eL zTOV7TvOJBuO6f/Lxx4xn505+c2//jcbnTafTTzBM7+m1V+r63Zfay457Civ/TLpr3/PsOMt8es/ 8/oxI3ZV53Dd4N+5/m/OfOp8tvKnk3bLbTD8KPWv66+N8eB8tpGvH08ZrK6btJt6tmFGqX994uGD v//RA4cdZXXnHJN/vsOlo0zzq7txNp3a/+8ov3Ir/+9umuzzHX7367/BJBuO211uR/qvLeO/Vn8f v3kd81dT9us/d7X/9/O/89kOv/0+63+/qq9/bF/V/6///9j/+OsR/3/+//N/+vf/7/76ks75fM04 qLuJW9bgd9N1i7d1mEv/e9H6/+t/d6rq0lcJfwp++3vqry9VvdRsL05N+Nu/xyTdp//jf2HPefO/ zv/zP/+dpv4f2f83+xjLi+sTUn08Ur+6TEn18Q8PO9CUVB8jeNj9pqT6WMXD9jAl1cdEXtyekOrj 8PpprCipPurv/dqEVB9jeNgdpqT6mNWLcxNSfTzn62dTUn2cVZ/1i5Lq4xsPezwh1cejHvZlQqqP 8TzsNFNSfZziYdOZkupjKg+71pRUH1v4+lNRUn185WEvJ6T62N7XzEVJ9TGqF3clpPpY0IujE1J9 zOHFaQmpPn709ZQpqT5G8uLOhFQf23mxRkKqj+897PWEVB/1a+MzU1J9DOlhl5uS6qOevjjJlOTv H88kpPr4tj2/RVJ9HODrz0VJ9bGwFwcnpPqoJ+WGNSXVx1O+PjYl1ce2XqyVkOpjHS+2Skj1MYwX DyWk+tjAi80TUn383sMuNiXVx2Je7J+Q6mNNX3MWJdXH+b6GL0qqjx09bGFTUn2UMjj/Eok9/+HF lQmpPk73NWlRUn3Uuz9TFCXVx8pe7JyQ6uNCX2MWJdXH6l7skLA/79Cfd6g+bmlnpCKpPtb2sO1M SfXxOw8715RUH0fW3KKk+tjVw+YxJdXHXO3nSSTZx1EJqT7e8/WQKak+6t30hUyJPV/oYf8yJdXH 5+0OYSTVR927fjEh1ceMHnaMKcnn109JSPWxhodtZEqqjzPrP1+UVB8XdYP76ZFUHyt6sUtCqo+Z 2vfPSOx5qbafH0k+b/lDQqqPFz3s/YTY/X0Pu8qUVB83dIOeH5HY85bt/k8k1cddHjaiKbH351qP rUiqj+U9bHtTUn3M4sUZCak+rmjnKyOpPp7w9awpsf2Cfb1iSqqPJb3YJyHVx3Je7J6QfB733wmp Po5v500jqT4urnlFSfWxuBf7JaT6qL2SfzEl1cefPewoU5J/vlyfkOrjdg8b25RUHzt72KqmpPrY 19e0RUn1cUQ36OEYSfXxkoe9m5Dqo/Y6PTEh1ce5rad2JNXHze1MYSR2flR7hxyJPf/hYfuaknw+ +TxTUn185+tGU1J9fOBhbyek+rinG/Q7jaT6mNDDTjcldn+unQmKJJ8/3T0h1ceq7cx6JPm8wwkJ qT7q3bBRTUmej3xVQqqP/3rYfxNSfYzZZmhFUn0s4sWBCcn3TZ9KSPVxnYcNb0qqj809bCVTks87 HJAQ+3m9zViLpPr4sp2vjCTff6kzoyKpPhb1sC1MiZ3n6cV6CbHn+T1sZFNi5zd42NKm7O839Pcb qo8TPGxKU1J9LNTmAUWSP398Zkpsf0svbk1Invd6rSmpPp72sG8SUn0c62uqoqT6+LTNI4yk+tjB w1YzJdXHs+17RiT5/fqLCak+hvLi3oTk+R7jFCXVxyht/l4k1cchbb8lkvz88lhC7P1sD1vClNj5 cx42tympPg7ysNVNSfXxgIcNZ0qqjxM9bCpTks9rn29Kqo/R6xl+U1J9TNZ6fkRSfZzW9lsiqT7m 87BdTEn1MZGHnWVKqo86G2maoqT6eNfDPk5I9bFK6z8fif16aWekIrHzTT1sN1NSfdRnlStNSfUx g4cdYEqqjyk87BJTYufhtK+RSKqPZT1sQ1NSfTzp6zlTYvvleNgIpsTON22fNyLJ8+eOT0j1sUn7 /hmJPV/YzntEUn3U3jjvmBL7+bTNbIjEzpv3sEVMSe6n9KMpseeDPOxWU2LPW7Y7ppFUH2t62Gam pPp4rP18jaT6eNnD3klI9fGeh72UkOqjngW60JRUHwe0PexIqo9J2h3TSKqPW9r99Eiqj9G8uCkh 1UctnkhI9fFmO98QSfWxlodtY0qqjzqLcIaipPqYpp2vjOznR/Xzo6qPxVr/tUiqj508bH5TUn28 4OspU1J9LOVhW5sSe5/Qwy4yJfm++jMJqT628zV7UVJ9POfrRVNiz9N1g57rkVQfS7fnt0jy/ew/ mpLq45n2/SKS3C/nI1NSfQzhYdeYkurjlDaDLxLbL6ftuURSfdRZDc+Ykuqjvgv7wpRUH7t62Lym pPp4sO25RJLnaY1hSuz+vheXJCTf3z/JlFQfX/i625TYecAe9mhCqo+FW7+PSKqP2dtnjkiqj4fa 59FIqo/6s2QaU1J9XODrZ1NSfZxT3wkVJdXHMR42rSmpPj5ue1CRVB9re7FVQqqPRzzs24RUH4+2 +2GRVB9berFuQqqPyb24MCG5/8fQpqT6+IMXZyWk+pjXi2MSUn3s5mumoiS/X5/ElFQfj3vY5wmp Pupe/t6mpPo4t9ZFSfUxVjvzEYnt7+Br/qKk+pjNw/Y0JbZ/kK+xi5LcT2l6U5LPa/+uKKk+dm/n gSKpPr5u78QiqT428rB1TYn989HuEEZSfbzYnt8isedPPWxYU2L357pBf75I8tfLewmx7089bHtT kvsHXZ+QvB91QUKqj33rmdyipPr4st15iaT6qLNNxjYl1ceebf5vJHl+w8GmpPq4sZ0njKT6WM6L PRNSfWzrYauYkupjHV8zFyX5+WU7U1J9jNz6nUZSfdS9lv1MSfWxvIf9w5RUH9d62PCmpPq4qZ2v jKT6WKbtuUSS5ze8l5DqY+v2GSyS6mPv9kwbiZ0H7MVpCak+lvRi/4RUH3U20mqmpPpYtD2/RWL7 S3nYjwmpPq72NVJRUn0cVp9xi5Lq45D2+48k70dNZkqqj6fbTLFIqo/X255tJNXHUB72sCmpPuq7 0uVMSZ7Ht6gpqT7W82KLhFQf97fP55FUHze087eRVB9Te9ihpiTfn9vDlFQfm3SD+SaR5H6fr5iS 6uM1D/smIdXHQe38bST2ea7dmYuk+tjYi40Tks9rv5EQ+/PWi40SUn2M78W1CbH7+x62hCmx59db T4dI7PcPD1vRlFQfx7X+0ZFUH3u1/adI8ry1101J9bF5O1MYib1f2WYiR1J9rNXOZ0dSffynG/Sj i6T6WMyLAxOS5xPObEqqj/d9vWpKqo86+/c0U1J9PNnep0dSfZzua/iixJ4v9LAZTEn1UX+3t5uS fF99t4TYefPdoGdQJLafkoddakqqjw292DQhdj6Qrw9NSX5/+mdTku+L7ZsQe37Mi4sTUn280Z5X Isn3bxczJdXHS63naSTVx7vtaySS6uP7er8jIbbfVn1HVpTY+bceNp4pqT52bT22Iqk+zqj/fFFS fZznYeObkurjp25w5yWS6mPaNkM8kurjLV8PmRK7v+9hQ5qS3B+3zjiJpPp4sxvc2Y+k+virh21j SqqPWzxsBFNSfTzUPnNEYvdfWs/TSGw/aQ9b2ZTYeWvtflgktv+HrwmLktwfd1hTUn08WPdgTEn1 8UI7XxlJ9fFnL05JSPUxVZufFUnudzFnUWL3X7xYKyG2n6OHzWdK8n2g9UxJ9fGdhz2RkOpjyNbj MxJ7H8jXcEWJ3X/xsANNSX6ffJ8pqT7WbvPVIrHzG1rP00iqj1k9bHdTUn2c7WETmpLcf33yoqT6 +KHdaYik+jiqG/Tni6T6eNvXc6ak+liozbCIpPqYqJ05jcTej+oG814iqT6+9XWNKcn3xfZJSPWx ohc7J6T6WLztYUdizyd72AMJqT4mafcpI6k+/u1ho5qSfJ7/elNSfZxZs4qS6uP51hMmkupjvtYf OJLq43MPey4htj9dmzkXiZ2X5OsTU1J9jOVhJ5uSPE9rGFNizxd62J6mpPo42NfYRUn1Uc963J6Q 6uPSbvALkVQfl/n60ZRUH1N4cX5C7PwoX3MUJbm/5ZhFSfVRz+6PWJTkzx9TFCV5f+4eU1J9bO9h C5qS6mOX1j8pkupj4rbfEkl+H/SpKcnnYY4xJdXHTO0+ZSR53utGCcn9ts5KSPXxjYc9mpDqo/Zy uCwh1Ufdm5ygKKk+jukGM4AjqT7+6cWaCbHzgdoZqUiqjx1bD7ZIqo8VvNg9IdVHDXvOlFQfV3nY 5Kak+hjHBucJI7H9ctqfiUiqj5W82CUh1cf8XhyREDtf3cN+SIj9eVsG/WAiqT7qs8q8Rdm/D+rf B1UfT3jY5wmpPmovmO8TkvtbPmVKqo/ZvDghIdXH5G2/NrLvZ9D3M6g+tvJi3YTk9+uTF2X/+bT/ fPrb/IbawzGS6mMfD1vSlFQfs3vY4aak+rjYw6YxJfm81Bmm7Pt/9P0/fvv8MVZRUn1M48XZCak+ Pmv30yOx8+bbjMZIqo/XPeydhFQfM3rYUaak+li69QeOpPoYqd0/jqT6OMLD5jYl1cfUXlyYkOpj ei/OTUg+LzWuKak+DuoGd8Qiyc/7x5uS6uNLXzebkurjdA+bxJRUH8d62HSmpPqod0ufTUj1UZ/t HzMl1cf99fduSuy8aA9bzZTkeeLrmhK73+BhO5kS2x+3G8xDjqT62MbXzEVJ9bFAOx8VSfWxoBeH JqT6uK4b9EyOJP/5OCQh1cdqXmyXsJ/f0M9vqD5W9mKHhFQft7U9/Uiqj/W82Dwh1cfOHraYKak+ /ttmREeS97NvSUj1UWc1vJSQPI9vv4TkftKzFyXVxx6+pipKqo/vfN1iSuz5Dw870JTY5zlf35oS 27+w9X+NpPoYxos7EmLPF3aD+wyRVB8beLFpQqqPx9v+UyTVx6JeHJCQ6mOx9vuPpPoYz4srEpLP r89sSuz8qHbeNJLqY99u0M8hkurjFV9PmpLq4x5f75iS6uOBNiMpkurjbA8b35TY/trdYIZFJHae p4eNYUqqj9+1/adIqo+z2jugSKqP5dsZ7Uiqj4fbHnYk1cdm7c9EZP+83z/vVx+/1B5sCak+NvSw lU1J9fGMrxdNib0P1A36N0ZSfRzta7SipPq4y8N+Skj18V47LxZJ9TGphx1pSqqPS3z9bErsfeRu 0HMskjz/5aOEVB9TenF+QnJ/qXMTUn3U750PJKT6+NrDnkpI9fG39n4wktyP/oeEVB97e9g8psT+ fPGwg0xJ9bGUF3snJL9P/lfCvt9432+8+jjS1xhFSfUxgxenJaT6qM+yt5sSe7+y7VFGUn0cX7OK kurjhDYzO5I8L/rwhOTzQSMUJdXHDq1HXyTVx6ndoKdDJNXHie1OQyTVx588bC9TUn3c4OtjU/bP c/3zXPVxYTszFkn18UcP28+UVB+3tPmukVQfu3jY/Kak+ljFi+0TUn1c4WGjmJLqY6p2viGS6mPt +u9QlFQfJ7c9uUjseX5f15mS6uO+btCzMBLbH8bDhjAl1cdKXuyakOrj/DbjNZLq4/t2Xj2S6uPm 9j49kupjTA+70pRUH9e0GY2R2PNSHranKak+HvX1oymx/ek8bGtTUn284+teU2Lv73eD+VmRVB+f t3fKkVQfh3jYbKak+tjOizUSUn3Uuy4fmZLq4xRf4xcl1UftvXahKak+PvT1nCnJP1/mNyX2flQ3 OLMeSfUxiReXJeznRffzoquP2gv3i4TYny8e9mJCqo9t65nLoqT62NrXLEVJ9TFi6wEbSfVxdzs/ F0n+vH6PKak+xvXi2oTY98ke9kZCqg8rgz0XIfU8nYetb0qqj0M9bG5TYs/j+hq6KPv+MH1/mOpj y24w7zaS6mM+D9vVlFQfJ9VnmKIk97u4x5RUH3X23oRFSfWxkBcHJ6T6qLMr3k5I9bGch21pSuz9 bA/7nSmpPjb3Yv2EVB8H1dyipPqoe/mfJaT6+NLXHaak+rjT16emJPf73Cch9vtH28OOpPr4q4dt bEqqjyXaTORI8v2oU02J/fPR+llGks8X/smUVB9v+nrYlFQftRfM9EWJvf/SZvBFUn1M2PqtR1J9 zNj6aUdi54m3Mw6R2P64HjaZKak+6lnkm0yJnS/mYYebkupj47bHEIntX9gNerBFUn1s4mvWoqT6 WL71T4qk+qhn53Y2JdVHnU0wVlFSfSztYZuakuqjPtufkZDq4zYPG9qUVB8rts8ckdj5cx52iimp PupdyqdMiT0P4+svRUn1MXLrWRiJ7c/fDfrBRJLnI//DlFQfL3nYuwmx8ys9bF9TUn1s0N55RFJ9 TOHFeQmx/Qvb+dvI/rxUf17qt3nR5ySk+jjCw2YyJdVH7X1yYkLyfaC3ElJ9zOHFsQnJ+/sTmZLq o77rOCEh1ccF3eAXIqk+hvew80xJ9fFKO28aSfUxuoedZkqqj3q28jtTkvvR32xKqo9hPOwiU1J9 rOVr3qKk+li43UGOpPr4ydfVpqT6qGejFjIleX//ZFNSfQzpxT0Jse/X2zvkSHK/8U8TUn2s3npq R2LnA3nYwqYk93Oc3ZTkzx/zm5LcP/mVhNh+OR72ZEKqj//Urw1TkuebvmhKcr/P/5iS6mOZdr8j Ejv/pfVAiaT6eLf9fI0kP899lpDqo+61PJKQ6mNHD1vAlFQfI7UzH5HYeXy+5ipKqo+b2v3BSKqP ehZ5tqKk+ris/UyJJO9XHpiQ6uMwD5vRlNg/Hx62tSmx/XK82Cgh+fnl84RUH9e1+QSR2Oc5X9eb kurj1m4wEzmS6qOe3T/dlOR+fS+bkurj392gf1Ik1cfX7X1pJLa/dje4UxlJ9VE/a9xnSuzPl9Yv OZJ8HmYpU5Lfn85XlFQfW3nYuqak+hi19U+KpPp4z8NeSkj18QcP29+UVB/ztp6nkVQfa7bzyJHY eScetrgpyfuVo5mS6qOerbzXEkJ9LO9hu5iS6qPOhn7JlOT3QS8mxPbr8zVnUVJ9TOvFuQmpPoby sBtNSb7/8mZCqo9v252GSKqPlbzYMSHVx8oetpYpqT7q7/ZOU/bzG/r5DdXH7r7+WJTYz6ceto4p qT4WaO8HI6k+6ruw3UxJ9fGah32YkOpjbS+2Tkj1MY8XRyXEzldv/ZIjyfezbzcl1cfz3eCMdiTV xw8e9nBCqo+ZW//5SGw/2LYfF0n1MZkXFyfE7me359lI8ufTrRKS5xVMbkqqj2PbfcpIqo9j6t9b lFQf87f3P5FUH6O086aRVB9Pd4P7UJFUH/Vdx9hFSfWxf80tSqqPTzzs2YTkPx8TFiXVx1Qedqgp qT4e9LBvElJ9LOHFvgmpPu7oBj0LI7HztNq87Eiqjz08bF5T9vNw+nk4v31eH6coqT4WajMKIsn3 b5cxJdXHFW2/JZLq40IPG8eUVB/12e3ShFQf47f+FpHYfhf191yUVB8jlEHPsUiqj5G9uDEh1Uc9 6zFSUVJ9HOdh05iS/HlsVFOS+ynNbUrs/m2bURBJ9XGor/GKEvt+rO45FCXVx2heXJ+Q6mPDbjCf IJLqY5t2ByiS/PljZFNSfcznYf80JdXH0e17aCS5X869pqT6qGdfnjIldp6Fhy1nSqqPa1vP5Ejy /ZcxTEn1Uc/efmpKqo9VPWxtU2L7F3pxX0aoj/os+4UpqT6WbT1QIqk+zvew35uS6qOe3b8yIdXH xO1+aSS2f5AXmybEzpv3Ys+EVB/12f6HhFQfr/p62JTY/g4etpcpqT7mbP20I6k+TvKwKU1J9fFl N+jJH0nuT7elKcn7LzuakurjnPrPFCX5+XZcU2L3b7vBjIJI8ryC2YoSe369nbGMpPo4wteYRUn+ PHaDKak+hms/UyKpPursm0dNSZ7/clbCfp5FP8+i+njG19OmpPqYzcN2NyX5fuVlCak+9mz3OyKp Pv7kxckJsfMavdgtIdXHmb6GLEqqj3rW9OOE2P6n7T5lJHaeuBdnJKT6WN3yhZ0/58UOCcn3oxYz JbYfWzvfEEn1MVfrsRVJnhf9eEKyjycSUn3s185YRlJ9zODFaQmpPkb3sDNMSfVxi6/PTEn1cbKH TW9K8nyPaYuS6uMNXx+Yktyf/7WEVB/1WWUoU5LfF36WkOrjqm7Qoy8Sez+7G/S3iMR+P/V1hynJ 86NuSEj18W03mP8b2T/f9s+3/2h7k3clpPpY2ot9ElJ9zNT2sCOpPl73sE8TUn1M2e6nR1J9XOlh E5iS6uOebtAvKJLqYzcPW8SU5Pu305mS6qP2Fr/YlFQfn/t60pTYz2Meto8psd8/6q8VJdXHsF7c lpDcP3kkU1J9bOTFxgmpPhZsMwoiqT629TVrUVJ9jOVhF5iS6uOvbaZYJNXH2e38fiT5feEZCcnz ot9LiD2/7sXaCbH9UDxsZVNSfazpa/6ipPrYtM0niKT6OMDXBEVJ9XGgr98XJbb/aZv5Ekn1Ue/+ jFuU5PdBY5iS3K9vQlNSfdzt60NTUn1c3OYTRJLniz1sSqqPelbsI1NSfdTZ8vVOQyS5P/+PCak+ 1vewFUxJ9fFmu/8TSd5vONmUVB/n1rooyeeDzjQluf/6kEWJ7c/vxeEJqT4e8/WyKcnvx95NSPUx goddZEqqj1naGbpIqo/7fb1lSvL7j/tNiX3eb/f1I6k+Tm9nTiOpPi709bMp+36ffb/P6uM2Dyum xN6v9PWgKak+xml3oiKx54O82CYh1cfB7bxHZN/fsu9v+Ws/FA8715RkH+eYkuqjnlU/zJRUH6e0 +b+RVB8rerFzQnI/pWtNSfWxhIdtZkqqj828WD8h9vO6h61qSqqPRT1sC1NSffyx9V+LJN+/naEo qT6WbD9PIqk+LmrvjyOx8/ha/5NIqo961mOsoqT62MTDljcl1UedLT+tKak+am/gOr8ikvz1sqwp qT5mbz36Iqk+aq+PSYqS6mPG9nkjkvx5bC9TUn3UWS8vJKT6qLP3njMl1UftVXhLQqqPZ309bUqq j3rX5Z6E5PtzK5qS6mMiDzvWlNj+lu0+ZSTVxzwetpMpsfuVbcZrJNXHax72ZkLs59PWYzwS+37M w4YxJdXHnh42pympPuq74wNNSe7HNl5RkufxXZ+Q6mNdL7ZISO6/fnBC7P6th81gSqqP7+tM5IRU H3d62C8JsefXvTg7Ifb9qYd9nJDqYztf0xcl1cdSbc82ktxvfL6ipPq4qfUviKT6mM3DdjEl1Ud9 VzphUVJ9POLrRVNi++V42HcJqT5GbDOBIrHPL92gf1Ik1Uft7Tm5Kak+zmx72JFUH6d62GSmxJ4v 9OLkhFQfK3ixa8L+PmF/n7D6+MbDHk2I7afkxbUJyfOiH05I9TGaF7cnJD/ffmdKqo992/vBSPJ5 qZ8SUn2872FvJCT3P633jyOpPursvSsSUn3Ud6WfJqT6uMPXu6Yk78/NW5T9+eT+fHL1sZgX+yek +hjCi/sSYr+ftj2XSKqPOjt8R1Ni+xl42FKmxM4D9jVmUZLP032SEHt+3df8Rdnfr+zvV/6jfa+4 JiH580dnSqqPQ9qeSyTVxx6+Ji9K7M8XD/u7KbH9pbw4JSHVx+5tTz+S6mPKMugBG0n1sXnJSfVR 35UelZDqY3oPO9SU5H5K65iS6mNsDzvLlFQf2/uauSipPhb2sO1MSfWxT/31osT2H/Ni44RUHxN4 cVlCqo91fM1elFQfq3vxz4RUH3WW6Z+KkurjOV/PmJJ8/nSyoqT62Km9/4mk+virF3smpPq4z8N+ Tkj1MZcXRyck788NYUpy/8KJipLq4yUP+yAh+X3y4QmpPurs3+FNSb7/8mJCqo+VPGwtU5I/fxyV EHtf3cP2NyXVh/12Xj0S6uMgX+MXJbY/XTeYzxiJ7f/hYRuakupjYg873pTkny8HmZLq4+L2MyWS 6mNSDzvGlFQfH7V3QpFUH7f5es+UVB+HdoPz6pHYedG+ZilKqo9/+frWlFQftffa8EVJ9bG0F3sl 7Ofx9fP4fvXhYVuYEttv3MNmNyXVR+0NfJQpsfOS2uevSKqPx3y9bEqqj1G9uCEh1ceGvmYtSqqP 4zxsalNi92/b+45Icr/gKxJSfZxYf60oqT429bBlTIn9evGwk0xJ9fGur7tMSfUxftuPi6T6uKf1 S46k+tjVw+YzJXn/9gBTkvvzX5eQ6uMuX++Ykuqjfha9JWE/77Wf91p97NJ+nkRSfYziYWeYEjuP z9dwRUn1sbaHrWxKqo96t+M8U1J9jOfFvxNSfbzqYW8npPpYw4ttE1J9zOHFMQmx9/c9bEFTUn1M 1mYkRVJ9jNVm3kZSfTzsYV8nxPaT9rCZTInt1+dhC5mS6uMBD/s2IbkfyncJqT5Oac/3kVQfu3nY 3KbE3m9oZ6QiqT4u8fWDKcn3CX80JdXHFR42simpPnb2sPlNSfWxgYf9zZRUHw/5esWU2HnR7cxY JNVHne16oympPjZr5ysjqT6KF3cnpPr40tcNpqT6+K+H/Tch1ceHHvZ8QvI8i61MSfVxe/29m5Lq Y0Qvbk5I9VHX7EWJvT/na+SipPrIZleu2/f77Pt9dv9rnuepCak+jugGM6IjqT6Gru+QTUn1UXvP X5KQ6uPXz15Fie1/2mYAR2L7S7U920iqj9O7wTz1SKqPa+o/U5TY+2Iedqkpyf1gTzMl1UftdfpK QqqPW9t8pMh+3lo/b636ONjX2EVJ9fFaNzijHUn1cXX7GRtJ9fGVhz2ekOpj0TZzLpLq43tf95uS 6mOedl8ukjy/cgRTUn080u53RFJ91NlITyek+pikDHryR1J9bO5hy5qS6uMLX7eYkupjCy/WS0j1 Uc8SDmtKqo+tvFg3IdXHkF7cmbC/T9jfJ6w+fu/F1QnJ+7e7JcR+vbQzQZHkeRZvmZLq4z8eNpwp sc+33eCMdiR5PvJPpqT6mK2dSY4kz0c+wZRUH4t42DamxPZ38LAxTYntx+ZhR5qSPJ9wU1NSfdTe nnebkurj2TYzO5J8v2HcosTOV/ewlxKS+3+8ZUry/Ln7TEn1Mb8XhyXE+mg9giPJ88UeMCW5v/ax CcnvT18xJdXH6h62mimx+7cetrgpyfcrPzBlf167P69dfSzmxf4JqT42bu/UI6k+XvCwDxOS71de YErsfFNf0xQluR/siqbEzm/wNX1RUn2c2fYoI6k+1mzPK5FUH/f6esOU2POFbT8/kuqjvut4KyHV R/3aeD1h3z+5759cfbzZ/jxEUn1kd2+/B/vYpp35iKT6WKadf4mk+tjOwxYzJdXH1h62pCmx/aTb vOxIqo/6ex/PlFQfT7YZJ5FUH+942KsJsf1gPewYU1J93NnOi0VSfezhYXOakupjHC+uSEj1cb2v T0xJnqe1tCmx86J9vWpKqo+Pu8F9ykiqj5najOhIqo/h235+JHZ/rv47FCXVR32X/rYpyffF7jMl 1cde7fN5JHZ+gxd7J8SeX2892CKpPv7oxWkJqT6G8eL2hFQf27YeBpFUH5f6+t6UVB/1WWX4osS+ D2r9kyKpPub24siE5P3sRU2J7R/kxcUJqT7G8uKqhFQfU3rYYabs+yn1/ZSqj709bHZTUn1c5mGj m5Lq44Nu0NMykuqj9hr7gynJ/fq2NCXVx9gedpIpqT5G9bAzTEn1caiHzWRKbP9CL/ZNSPVxuYeN Ykqqj5W92CEh1ce47bxYJNXHRh62nCmpPkbysHNM2X8e6z+P/Trfw8P+YUrs/OxuMEM8kuqjzqo8 15RUH7t72FympPq40deHpqT6yO6aLtP3p+v70zUfZ3nYhKbs97P7/ezqYyEvDkpI9XG2h41vyn5e dD8v+tf+ll5slBD789bX56ak+pjQi0sSUn2s5cXWCak+tmzzkCOpPuZq78MiqT6uaGfGIrH9Puvv uSjJ/S0/M2V/P6q/H/Vrfylfsxcl1ceCHrajKak+9uwG948jqT42LzmpPur3imMSYu+re9hPCfv9 237/9tfzUr6+MiX2ed/XPEWJ7afUDWbORVJ9PONhXyXE7r+0eZWRVB/Pe9iXCak+Jmn3KSOpPiZt 79MjyfORHzBl/369f79efezmYQuYkuqjzr6Z2pRUH+N78a+EVB9jeNgppqT6WKDN9Iik+qh3sU81 JXZekofdZEqqjws9bFJTkvuNX5uQ6mOVdn8wsu+P2/fHrT529rCFTUn1sXqbaRpJ9fG0h32bkOpj Mg87ypRUHxO083ORVB/Hetg0pqT6WM+LzROS70dNYEqqj+d8PW5Kqo8tvFgvIdXHNK3nWCTVx9rt 82gk1cdvdywjyfeRRzYluV/wpQmx86M8bD9TUn2c7GvEoqT6qGcJn0xI9XGir5GKkupjBg/b35Tk +1Gvm5L8fn3eoqT6mNqLcxJSfbzSZs5FUn08Vd+BmJLqo+5N/qEoqT7O9zVkUVJ9jFcGd14iqT5+ as/8kVQf73jYawmpPn70sIcSYv98+LrHlOR+Bnsl7Pcr+/3K6uO8bvALkVQfX3vYYwmx5z/a+/RI qo/FvNg/IdXHnS0wkupjKi/OTYi9r+5hfzUl1ccU7Rk/kuzjgoTY+ZXd4A5yJNVH1stgIXj/5GcS Un3c5OtjU2L7Sbefr5HYfmwetpQpsf1Q2vnbSKqPepdhclP2/S76fhe/Pd/+nBDbP8jDjjYl1ccu 7Rk/EtsPxdfIRUn1sY6vuYqS6uP0+s8XJfb+frvjEUn1cXvr+RFJ9fGqr4dNSfVxfDc4nx1J9VFn qZ9hSqqP2gvmU1Ni+/N72JympPo41MNmNCX558tDpqT6qGc9njcl9ueLFzckxL5f9zVbUWLnzXvY kKak+pjTi6MTYu8je3FKQqqPAzzsL6ak+ris9TyNpPp4y9e9pqT6WKm9D4uk+ljOw9Y3Zd9vvO83 Xn1c5GFjmRJ7/9bDPklI7jd+mimx5z98jVCU2PnIHjahKbHzxL04KiHVx2pe/DMhuT/ucaak+tio fSaNJH8/nciUVB9f+LrRlP39266/f9sN+mlPbUqqj3HbTLFI7DwtL65JiD2v7etPRdnv3/b7t7/N 07rUlFQfdS9utKLE9jPwsC1Mid3P9vW+KbH9crrBfPlI8rzXqUyJ7XfhYYeYEnv+o91Rj+z3G/r9 hurjRQ97NyG2/7qHTWFKqo/hPewKU/b9xvt+49XHf7tBf4tI8jzgaxJi+322mXORVB8rth5Kkdj7 +15cn5Dq44/tvFgk+f7t+Kak+qizoh5LSO7HtqopqT4O8TVDUZK/Xm5NSPUxm4ftZkqqjzo7682E VB+beLFhQqqPz309aUrs+8L6zG9Kqo+DPGw1U1J91LvYQxUl1ce/PGxmU1J91J+tX5kSe37Mw242 JdXHD+0dciTVx99bD8dIqo9pPewIU1J9fNp65ERSfazta+6iJM97fd6U2P05DzvHlFQfV/gasyjJ /S5eMyX2+6mHbWNK8rzX1xNSfdxRf60oqT5m8bALTUn1cW/rvxZJ9bFdN7izH0n18Q8P29WUVB8r t5lAkVQfN7czp5Hk81IXJST3+xzClOT+DhObknz+dDNTUn28155XIqk+jvSwBU1J9XG9h41sSqqP P3txakLseZj2TiyS6uPcNp8xktwfdztTUn3M22YCRZKfX65OiP354mHnm5Lq42cPezYh1cd4Xvw7 IfnrZV9TUn280u7rR1J9bFX3YIqS6mOHbnD/J5LqY+rWgz6S6mOsdiY5kupjGC/uTIjtp+TFxQmp Pi73sLFNSfWxo4etYEqqj7t9fWtKqo8VvNgjIdXHcDaYZxqJ/XrxsB8TUn087+tZU1J9nNzep0di 57162LKmpPqYz8O2NyXVR9bL8UWwjztaj/FIqo9JW7/TSKqPob24KyHVx4RtfyESux/l60FTkucT TlKU5H59FySk+njAw4YyJdXH2+0+diT5/OlLCak+/uZh65mS6uOnNiMpkuqjnm2Yw5RUH3d52C8J qT7+6WGLmhJ7X92LrRNi75t6sUZC8uePjxJSfazS7pdGUn2MYoOfKZFUHy952NcJqT7O6gbzGSOp PmZon0kjsfNvPWwJU1J9bNveiUVSfdS966NMiX1f6OstU1J91Lvpq5uS6mPzdocwkvz5Y4SipPp4 uPWTiqT6+KS9T48k79/+x5TkfuM3mJJ8/rT2t4ik+hjVw64yJbafoxcnJKT62MDXrEVJ9fEHL85I iO332Q3mAUVSfSzjYZuYknx+bPiixM5r9LCZTEmeJ/6gKak+TvGwyUxJ9fFc26+NpPp4ps0kjMT2 P62/XpRUH6t6sVNC8vPtNaak+qi/9xFMid2v9LBFTEn1sYYX2ySk+ji99dOOpPr4pp3PjqT62NrD Fjcl1cft9fduSuz+rYdNaEqqj8N8jVuU2Hk4XmyWkDwfaFVTUn3s0u6IRVJ91FkNO5iS6mM3XzMX JfY+oa9rTUn18aSvN0yJnWfh6x5TUn284espU1J9rO7F9gmpPt739aEpqT7u87BhTUme3/BSQuzz beuHG0n1cVybwRdJ9TFPO08YSfUxt4cdakrsfaB2xjKS6uPZ9hk9kurjP+2+SyR53tqRCak+9m49 cSOx97N9/aUoqT42bJ85Iqk+ft/uQ0VSfUzmxVUJqT6OaGf4I8n9lD5LSPUxkhf3JKT6WN+LzRNi 9yu9ODQh1cfr7fktkupjfA87wZTk+XPnJKT6eKEb3PGIJH//eCsh1cdR7TN6JNXHah62sympPpZu /fkiqT4m9uLKhFQfa3qxXULs5482DzkS+zznYduYEjs/ysNuMSXVxxdtTy6y77/e91+vPl6uZ1BN ie2n1M7vR1J9LNvmQ0dSfVxU66Kk+vi0fc+IpPoYx8POMCV23ny7/xOJvQ/kYUuZEjvf1MPOMyXV x9m+Ri1Kqo+6V/uVKbH9P1oPg0iqj5na10gk1ceMbX8ykuqj3i0dyZRUH7U38HEJyfsvG5uS6mO6 1vM0kupjeQ/b0JTY90Eetqkpsf22fN1vSvK8+Z8SkvvlbGJKqo9h235tJNXHnB52sCmpPtbzYouE VB+vedinCak+Hm/zbiOpPn5s/T0jqT6+9bBHEpL7jW+fkOrj3W4wUywSO8+z5CT/+bjHlNjPp14c nZB8nn+8oqT6+NrDnk5I9TGlh51rSmz/Qg/7MCHVx3Dt/nEk1UftZflDQvL7wmyRzye/akrsfSBf sxcleb/yAFNSfZzqYZOakurjxPYZLJLq41VfD5uS6mOv+nsuSqqPrXzNUZRUHwd0gxnikVQfN7Tz c5HY/jDtfnokth+Kh32ckOpjAQ870JTk+chfJ8Tuv/iauyix89XbO7FIcj+UixJSfXzl63pTkudH PWdK7Hn+9gwXSZ6vfqYpqT6W9GLfhOT3Y1OZkuqjnr2dxZTk/Yb5ipLqY+x2Xj0Se9+jnfmIpPoY 04ubEmI/n3rYzwmpPob04s6E5O+nJ5mSfB95I1NSfezvYX8xJdXH2h62iimpPt7xsFcSUn3sXs/E FCX2fraHPZ4Q+z7Zw441JXb+S+vBFkn1sbgX+yek+vil3R+MpPoYwsPuMCXVx0PdoB9dJNVH/dp4 yZTk96fzFiXVx/Ctv2ck1cc5HjaeKbH9k9v5uUjyPODZipI8X+y9hFQftdfYdwmpPurZ/YsTUn2M 4GGXmZLqY7/WYyuS6qO++5nVlFQfb7bnlUjyecsHTUn1sYeHzW1K7J+PNvM2kurj6dbvNJLqY8Qy OBMUiT0f1O5kR1J9/K6df4kkP8+NZkqqj/u6wf2fSKqPZ9v5uUjyfvZtpqT62KTN/42k+vizFycn JJ8/vSsh1cfl9Z8pSqqP2pvvDlNiz3/4utKUVB+n+ZqgKMnzkfdKSN5vuMOU2PmE7b5tJNVH3Zt8 zpTYz6cedrYpqT529bDVTUn18bmvl02JPS/la6yipPqYyIsrElJ9rOzFzgnJ+y+3JKT6OLntMURS fYzhYVeYkupjag870pRUH2N52DWmJPcPOjAh1cdSrSduJNXH8x72Y0Kqjy983WVKqo9jPGx+U1J9 3Olhw5mS6uPS9jM2EtvfoRvMBIokny/8NiF53snUpsTuz3nYJKak+ljLi60TUn282PZbIsnn6T5P SPVxZNuDiqT6qHdLnzAluZ/B3EVJ9VF7v/7elFQfe/v6Y1FSfazuxT8TUn38u54RKkqqj826QT/t SPJ5y+tMSfUxrhfXJaT6+NbDHk1I9TGDF6cmpPrYxcPmMyXVx/ft+2ck1cdu3aAfbiTVx9Yetrwp yec/jjYldr6ph51uSuz5MQ/7gympPv7YZiRFYvfn6jtDU1J9nNnmiUVSfdzr6xNTUn3M7mH7mBJ7 f9/XzEVJ9bGCh61nSvJ89fcSUn1M6GHHmZLcH/ethNj+/O18VCT2vEM74xCJ3d/3sDcSkvdvpy5K qo+/ebFrQqqPVb3YISHVxzZerJ2QvN9wsymx8029uDoh1cf5HjaOKcnzTq5ISPVRe2uNZMq+X3Df L7j62NHDFjAl1ccdvt43JdXHcl7skZDq44Ju0M8ykupjT1/TFiW2f5CHnWJKqo/5vTgiIdXHiu19 RyR2XkH7TBqJ3c9ugZHk/ds/FyXVxzrd4H5YJNXHZ75uMiXVx2pebJeQ6uMmXx+bkjwv+gJTUn1s 62umoqT6OMnDpjMluX/QmKak+tjSi3UT9vuV/X5l9VF7jV1tSqqP9bzYIiHVx3htvzaS6mMOD9vZ lFQf9WzlPaak+rjFw4Y0JdXHNF6cnZDqY2gv/pOQ6qPe7TgxIba/lIetakryfsPFpiT3H5uvKMnz s+9IiO1f6GvCoqT6mMLDTjQl1Uc9K7anKbH9xzxsNVNiv168OC8h1cdfPWwDU1J9zOnF0QmpPtZt n88jsf3YPGxfU5Lni51mSmy/rbbfEkl+n7yrKcnzs88zJdXH3z1sHVOSzztMY0qqj0292DAheR7w 5QmpPmb04oyE5PmV+ybEvg9q7wgjqT52bc/4kVQfxYv7E1J9TNZ+nkRiz3942JcJsefH2jvkSKqP jTxsS1NSfXzjYa8npPoYpv08iSTPR/6TKbHv173YMiHVx9HtDG4k1cfEXlySkOrjL20/PxL7vO9h /zQl1cd/fb1jSqqP+r1i1KKk+ljci4MSUn084utDU1J9nNPul0ZSfdzvYUObkurjrG7Q4zOS6uMQ D1vElFQfW3nYMqak+hjFixsTUn1c096JRfb9Yfr+ML/Na1zClNj3hd1gJnIk1cfPvm4wJdVH7R19 kSmpPmbx4rSEVB93doN+yZFUH3f7+siU5Pm3F5mS6mPeNt81kupjbS+2SYi9f+thM5qS7GM2U1J9 1Ls/k5qS6uMLX7eZkupj/7aHHUn1cUSbqR5J9fFmN5jhGUn1MV873xCJnW/qYZ8m7Pvj9v1xf+1H 3+6oR5L7ba1tSqqPnzzssYRUHzO1Z5ZIqo/DPWxmU1J9jNvmRUVSfSzrYRubsp8338+brz6mbmdg Iqk+au/o+U1J9VF7a/3NlNj+dF6sn5DqY4/2jB+JvV/pxcYJqT7qXewfTEn1Ue92vJGQ6uNFX8+Z knz/9s6EVB/TetjRpqT6qL0b5zQltv+ph+1mSqqPhz3su4T9vLV+3lr1sUU7YxlJ9fG0r2dMSe5v uZ4pqT7u8LAhTEn1sXS74xFJ9bGyh61vSuy8eQ9b0ZRUH9+183OR/f25/v5c9fFy/QxiSqqPxzzs 64Tkfn0rmhK7P1ffCRUl9v1Y6+kQSfWxlhdbJ6T6+LqdF4uk+qizbocqSqqPC339bEqqjwO7wYyC yP4+UH8fqPp4o/Xoi6T62NHXDEWJ/fPRnlkisfej2p2oSKqPp3y9YEqqj4t9DVGU2H5KvmYuSqqP 7T1sIVNSfUzTnlkiqT7qWbEPE1J9/OLr36Ykz6+8wJTk96fTFCXVxzJe7JmQ6uP59v0zEnsfuf47 FGV/v6G/3/DbfLHVTUn1MVe7AxRJ9fGJh72QkOrjsG4wHykSO/+lvT+OpPo42cMmMyX5feEzpiS/ X7/PlNjzDh62iimpPk7wNXJRUn3U3loHmZI872QJU5L7819pSqqPWtyXEDv/xcNGNiXVx2xeHJ+Q 6uN3HnaxKbH7Lx72YELsfVMv1ktI9bGAF4ckJPen28CUVB8TeHFpQvJ89dGLkurjPV93mpLq4yYP G8qUVB9jtn6nkVQfE7bvn5FUH/XZ7WxTUn1MXgZ3XiKx+1G+Hjcl1ceMbZ5YJNXHKq2/RSTVx5Je 7JOQ6qOezT7QlFQf+7V+yZHY/jBebJSQPD/7H6Ykvw/azZRUH+962PsJyf22djEldp5We0cYib2/ 32YAR5LPnz6XkOrj+7anHYn9vO7FwQn7+ab9fNPqYykP29yUVB9netj0pqT6qL0b5yxKqo+/ebF7 QqqPebw4NiH5fOETCak+jvWw2U1J9XFAe2caSX5/uoQpyf2kbzcl9r56N+iXHImdf+vFFQmpPuq7 43lMSfVxXq2Lkurj+HaeMJLqo7Q7HpHk/kHXmZLq4/M2IymS6mNbD1vJlNh+474eMGXfP6jvH1R9 jGaD+6WR2P7JHraMKcn3TUczJXbemhd7JSTPbxi6KKk+6uzOExOS50UfbEryfuWEpqT6eN/DXkpI 9TG1hx1lSmw/aV8vm5L8fv0FU1J9TOFhx5mS6uNSDxvXlFQf43hxdUKqj3r2ZdqipPqoz25TFSX5 89jLCak+bvawYUyJPY/ra8yipPo40cOmNCXVR3Y2eSmwj/90gztikVQfc3vYzqak+pi4Pa9Eku/v 75uwn3/bz7+tPtbpBmfWI6k+pvTigoRUH9d3g5nqkVQfM7c7yJHk/tpXmZL8fuzKhOT7c38sSvJ8 wqmLkjwPeIaipPr4uBvcd4nEzq/0sI1NSfXxjYc9lhDbf719BovEfj/1Yu2EVB+bedhypsT2t/Ri h4RUH/Vu+qumpPrY0MNWNCXVx0++rjUltr+Uhz2SkOrjLl9vmxL7/dTDPktI9fF6N7gfFok9j+vF OQmpPobw4u6EVB+/9+LyhFQft/t6z5RUH1e2/afI/rxDf97ht/7rGyYknx9bzpTY/RcPW9CU5Pu3 eyek+nilG8wDiqT6GNuLqxJSfdSzcxMXZT/ftJ9v+uv9udZzLJLqY4n2NRJJ9fGUh32akOqj7j1N V5TkeSe/K0ryvJNZTEn18YWvW0xJ9bFC+7wRSe73OVpRUn1s72v6oqT6eKntyUWSfTxuyn6eeD9P vPo4qO1BRVJ9/N3D1jEl1cdEHna0Kak+7vCwXxL2+1H9flT1MaIXNyUk34+aviipPupZj3qnIZL8 PmjEoqT6OMzDZjIl1cci7TNpJHY+kIedYkqqj1s9bChTkvcrNzIl1cct3aAnXSTVh3nYZZYQ6uOy Np8gkuqj3v0Z3pRUH5+1+UiR2O8fXtybEeqj9vo4PSHVx3gedrwpqT4ea3vYkeT+64ebkurj3PrP FCX284evr0zZP9/2z7fVx1TtaySS6mN5L/ZISPXxQTeYbxJJnofztimpPoZtMwkjqT4W9rAjTEn1 UffynzIldj5QN+jxGUn1sbgX+yek+vhbm5kdSe7/cWFCqo+6d72fKak+Hm0z1SOpPt7zdb8pyedx JyxKqo+L2jvkSPL8uWmLkvz9tO5hR1J9PO7rc1OS5+HMUJTk/qfrm5J8nu4KU1J91LvYtyek+njD 1/OmJM9L+saU2PPa7fN5JNXHau2ORyT5/dh6pqT6qGfnnjYl1cezHvZRQqqPlb3YKSHVx1ptHlAk 1ccjbQZfJPb7R/s8Gkn1MXJ7Xomk+jjc16RFSfUxvYedaEpyv8/pipLqo+5dL2VKqo91vdgqIdXH ib5GL0qqj7N8DVmU5PlRDyUk9x970pRUHz/Ud6imxPaXamcKI7GfP3z9uSipPkb14uaE5HknfzMl 1cd33eBOVCTVxzQedowpsf3HvFgjIdXHZF5ckhD7ft2LrROS+2uPXJRUH3V25xBFSfXxdTtTGIl9 3vd1tSmpPvZrz3CRVB9TenF+Quz+fuunHUm+L3ZuQqqPzXzNWpRUH5942AsJqT52rc+4RUn18Y2v m01J9fFQ+wwWSfVR35V+bEqqjwd8vW5K8v7tUEVJ9TGPF0ckpPrY28NmNyX5/NgBpqT6GMXDzjIl +fzHwwmpPuby4uiEVB+re/HPhFQfm3qxQUKqj3972BimpPrYxtefipLc73O3hFQf57f9uEiqjwW9 OCQh1cf67XxUJNXHXb7eMiXVxxltpmkk1ceD7R1yJHb/pZ0njMT2k/awDxNSfSzR7sxFUn3s6Wvy oiTPFxvTlFQfr3aDGTiR2H4oHvZZQqqPd9ufiUjs/dt2RiqS6uPJ9vURSfXxL1/fmZLqo84Ovykh 1ceE7X5HJNXHob7GLsr+flR/P6r6WMPDVjcl1Ued7fpfU2L783vYLKak+pjTw3Y2JdXHUl7snZDq 4wsPeyoh1ccqXuyQkOrjNA+b3JTk8/zXmxLbb9zDhjMleT7QeEWJ/f7ha5iiJM83Pd+UVB8/doN5 HpH959P+8+mv96PaPPVI7P6ch72TkOrjmG7Q3zOS6qOeFXstIbn/+jOmpPrY3tcfipLqo97tmKEo sfPWvLgyIfb+i4cta0qqjws8bBxTkvf3vzEl1Uddsxcl1ceFHja2KbH3xTxsMVOS+2tfkpDq46q2 BxVJ9bF46yEdiT0f5GEzmbLvf9r3P60+Pm/715Hk++qjm5LqY6U2rzISe167G8wjjCTP95ihKKk+ 6vfO50yJfX7xYu2EVB9TeNjlpiT3dzgiIdXHa22PMpLq48s2Uz2S6uNcD/uzKak+zm7fQyPJz7cT FSXVR92rPTshtt+Wh21kyn6+Rz/f49f+Yx42rimpPn5qPbUjqT428bCVTEn1sZOHrWBKqo9ffN1n SqqPcdrzfSTVx1a+5ixKqo8FPGwvU5Lfn75jSqqPtdv8zkiqD6t39i0h9eeLF9cmpPqY2ItLE1J9 /K69I4yk+vi5G3z+isSeT66f2U2JfR/kYXOZkurjJF8jFSXVx4m+xi9Kqo8jfU1alFQfdS/uCFNS fSzc5jVEUn187OtRU1J9vNcNep5GUn0s13qMR5Lv73+YkLx/u74psfMJfV1tSqqP9bzYPCH2523r YRBJnl95VEKqj8N8/b4oyfeBnk1I9XFFm28SSfVxcJuXHUn1cWY36MkfiZ1P6MVmCak+VmjzTCPJ /S7mLEqqj7+0d8iRVB8XtzOWkVQfs3rYbqbE3jf1sEVNSd6f+11RUn3s2M7QRVJ9nNz+PERif962 85WR5H7S15oS2//D1w+mpPqYoc0EiqT6+KEbzGyIpPqYrvWUiqT6mLb9/iOx+3Me9mhC8nzkTxJi zwd52FamJPe7eCIh1ceqbWZlJNXHUF7cmZDq48V2ZiwSe/60vQOKJD/PfW9Kqo9dPWx+U1J9jNLm qUeS76ufakqqj5E87DxTUn080w36WUZSfezWvn9GYucjd4OZc5FUH3/ysL1NSfXxSfueEYndr6zv DIuSfB7m+IRUH9e0M7iRVB8LtRnRkX2/vr5f32/9tQ83JdXHYx72ZUJs/2RfQxYl1cf0XpyRkDw/ exhTkuffTl+UVB+3etiQpqT6+MjDnk9I9XFle0cYSfXxtoe9khD7eawbzIuKpPq4zde7pqT6WNKL fRJSffzNi10SUn3U3q8zFSXVx7rdoIdBJNXHTe15JZLq4xEP+zoheb7paKak+hi+DD5zRFJ97N8N 5t9EYs+ftncekVQfG3mxUUKqj7o3OVJRYucV+Jq7KMn3gQ40JdXHBB52rCmpPt7qBvMrInsfvY/q 4552JzuS6uPU+s8XJdVH7T3/r4TkeThXJiTPAx6yKKk+6rv0SYqS6mMYL/6TkOpjzjbDM5I8b+0y Swj1cbWvz0xJ9TFf65kcSfVxma/vTIk9T+frA1NSfSzoYduYkurjOl+fmpL8fn3jhFQf9Wfr0wmp Pl7ysHcTUn0M4cXdCbHnLX3dZ0rs+SAvtkhI9bG0h21iSqqPVTxsTVNSfczrYUeakurjXx42jSmp Po7xsIVMSfUxZntfGkn1sbGHrWVK7PsxDzvelOR+n1ubkvz8cn9Cqo8XusGM10jsfGQPezkh1cdU rZ92JPY8jIdNakrs/ku7zxBJ9VG/VzxqSvJ5h7sSkvfnrCipPuq749ofOJLq49A2PyuS6uOWbjAP KBL7/FLPwJiS6uMND/sgIdXH5h62gimpPu5s/YIiye+T/2BK8vmgf5qS6mPqNmM+kupjL1+TFyXV xxwetospqT6+8rAnE1J91LDrTYmdd1JnqpuS6uOoNlM9kuqjzlbbwJTY/ezW3yKS6uP1dt40kupj Wy/WSkieX/lsQnK/4KFNSfVxcDfoJxVJ9XGJr59NST5vOaopqT4Ob2cKI7Hn+T1sJVNSfdR3g0uY kurjgm7Q3yKS6mN1D1vPlOTnl3cSUn0s0uZnRZL7je+akDxfbHxTUn2M4MWtCbH96D1sSVNSfdze euREUn0M2fYXIrHztNp9uUiqj1887L6EVB/H1ayipPpYx8NWNiX254uvD01J9fGgh32XkOpjTS+2 TYh9n+zrJ1Ni9/fbn4dI8nn+j01J9TG/h+1gSuz7dV8zFCXVx5+9OCkh9n5DyUn18aaHvZawn0/Y zyesPmrvxqdNSfUxsRcXJyT3M5jMlOT5Lz8npPqovcXHLUrsfmU7nx1J9bFC+/1HUn2M7GHnmpJ8 HmYtU5L7bT1lSuzXixc3JqT62LKdJ4yk+jjB14hFST5/uogpqT7W8zVnUWLvq7c72ZF9P7a+H1v1 8Wz7vBFJvi82lCmpPoYrgzMOkVQf03txRkKqjytbD4NI8uePuYqS6qP2PnnelFQfm3rYX01J9fFa mzEfSfVxkodNbkqqj6s8bERTYs/j+pqnKKk+Lm+fNyLJ/U//mxB739TXA6bEntfuBvM8Iqk+7vew 7xOS+30eakqqj0c87KuEVB/DethFpqT6GN2LaxNi97Nbv/VIqo+d2xn+SPL7wpFMSfVRvLgnIfb9 mBcbJKT6qO86zjYl1ccH7YxUJNXHDr6mK0qqjzpb/s9FSe639UZCqo996u+5KKk+zvKwCU2J/fni 6w5TUn0c4WEzmJLq44HW3yKS6uOTdmYqkupjdi+OSYidp9V6jEdSfdSfrUebkupjiXYGJpLq410P eykh1UedTXBJQqqPx9v5uUjs/ouHnW5K7Pv1bjBzLpLqYxovzk5I9bFjez8YSfUxT+uvFUn18bCH fZOQ6mOh9rwSSfXxWesZFEn18bavu01Jno88Y1FSfdTPojOaEttfyte0RUnen/s0Ifb9adtjiKT6 WNiLQxJSfazfemxFUn1M3masRVJ9LNn29COpPr5qz3CRVB+/b3cqI8nzcBY0JdXHAh62jSnJ815X NCXVx3ft+T6S6uMcX0MXJdXHlG1/MhLbn86LNROS3xc+ZEqqj5k9bF9Tks+PHZeQ6uPcbjDjNZLq Y4/2vjSSfB/5YlNSfdzgYcObkuqj3u24KCF2XpKHLWVKcn+YB01Jvj83R1FSffzDw9YzJdXHLG3e XCTVx989bDNTUn0s7sUBCak+PuoG9wcjqT5O8bCpTEnuR/+EKbH9C7tBj61I8nyx7MwD9v6Lh32e sL8P1N8Hqj7q3sK8RUn1cY2vL0xJ9TGbh+1hSqqPCz1sfFOSn+c2NCX5vPbIRUn1cWf9s2BKqo+6 d/1tQqqPrVsPg0jyfPXLElJ9DOXFnQnJ508XMiXVx+2+3jEl1cfH3aCfVCTVx49tZkNkP9+0n29a ffzg62pTUn3s2Q3uREVSffy7/hkxJdXHXd2gx1Yk1cdRHvZHU1J9rNj2WyKpPp7rBvOhI6k+/tO+ X0RSfZxX84oSe9/Dw15LiL2v7mGHm5LqY9F2PiqS6qP2thi3KKk+jm37LZFUHwe2O2KRVB+veNg7 Cak+vvB1sympPrb1sMVNiZ2X5GGLmLLvB9v3g60+nuwGMysjqT5287B5TYmdV+DFfgmpPoYrgz3K SKqPp9oMnEhs/3UPO8iU2Plz7cxpJNXHnF4clZDqYxQvrk9I9XGkh01vSqqP1bzYLiHVxzpebJUQ e3/fw5Y2JdXHVh62pCmpPg7zsJlMSfXxi4fdl5Dq47J2HiiS6mM8Ly5PSPWxe/31oqT6OKH+WlFi +xm0npaRVB9reLFtQqqPSds8j0iqj2VbD8dIcj/HC0zZz1fv56tXH5+2338k1cfKXuyQEHv+1MPG MyXVx0se9l5C8nz1VxJSfczY+q1HUn3UzxrjmJI8f+7AhFQfI3rY2abEzvfwsIVNie3P72FzmZLq 4/7WDyaS6uM9D3spIdXHEB52iSmpPr71sEcTUn3U3p43m5Lq42dfl5uS3I/+hIRUHxt4sWlC7Pkg D1vZlFQfY3vYyaYk71e+k5DqY8zWkz+S/Hn9xYTYfmwe9mzC/n1h/77wt/7r8xUl1cefPWxPU1J9 7NruD0Zi54l72CMJsf1PPayYkuqj3nXZ35RUH3N7cWRC8jytyUxJ9VHfDQ5lSuz5IA9b25TY90G+ 5ipKqo+jfY1alFQfZ/savyipPmpvrbNMiZ0H7MXmCak+lvZi/4RUH9+3nkGR5HkFjySk+visG8z/ jaT6+Eub2RCJ3X9p/ZMisZ/HPGwCU5LPBz2SkOpjyDKY2RBJ/n66mymx/dh8PW1K8v25p0xJ9XGV rxGKkuqjzmp4NCPUx7pebJmQ6mPB9vk8knx/bn9TYt+PedgqpsTON/X1p6Kk+vimfQaLpPpYqfVc j6T6+Kgb9HOIpPqYwItLE2LPr3txZULyectZipLq45j2ZyKS6mO5NvM2kupjYw9b05RUH/VZdvai JM9bG78oyfOSljYl1cd/fT1mSqqP+Txse1OS3wcdZkqqjxs9bHhTkvs53mJKqo+LfP1kSqqPw32N XpTk+0BmSqqP5b3YLSHVR+0V9HtTUn3M78VhCft+KH0/lN/2G3ZKSPVxSz0TY0qqj1vrZ1RTUn1c 23p8RlJ9bN3uzEVin19aD6VIqo83POyNhFQfR7Xnt0iqj/rZ/HhTUn38pwVGkvvl7G1Kqo96d/BF U5L3G3Y0JdXHid1gRnQkuf/HsKak+njQw75LSPWxUJtREEmeh/Nqwn5+dj8/u/oYvvW0jCT3Tz7J lFQf9bPXAqak+qizs2Y1JdXHJGWwpx9J9VHvpr9lSqqPTb3YICHVx8XtZ0ok1cepHja5KcmfP041 JdXHkR42gymx8yx8PW5K7PmgbtBzLJLqY3YP28WUVB9Dtz3byP58YX++sPpYzYt/JqT6OKfWRYnt P9Y+o0dSfbzf5iNFUn087OslU5L74z6ckOrjFV+PmLLvh9L3Q6k+1vZiq4RUH1N42BGmpPqYzosz E1J9jN/OE0ZSfUzmxQUJsfMs2hmpSKqPbTxsMVNSfUztYQeZEnt/zsNWMCXVx6oetoYpqT7W8GLb hFQfc7SeY5Hk/slbJMT2M+gGM8QjqT7+2nqwRZLnI89nSqqPt33da0qqj5t8fWRKqo9p2ozGSKqP Oquh3g+LxL4P8uJfCbH9T7tBf+BI8ryTezJCfazoYeuakurjGl+fmZLqYwYvTkuInX/bnlciqT42 8fWXouy/Xvqvl+rjQg8bx5RUH2d42MSmpPp408NeT4i9v+/rVVNizzt42AGmpPp4wMO+SUj28W1C qo+h2n2GyL7/WN9/7Nfzlh62timpPmZtey6RVB+Le9jmpqT6eM/Xnaak+rjHw35MSPVxiodNZkrs /KhucCY5kuqjtP2FSOzXi6/hipLqY/V2vzSS6uO8bvALkdj36+2MVGQ/H6ifD1R9jOHF1QmpPn72 sEcSUn2M5sW1Cak+5vLi9IRUH4+0d2KR/fyXfv7Lb/uVy5iSfD6ozvOIJJ/H/XdCqo8/tvOmkVQf f/Owk01J9VF/t6+Ykurjzm4wvyKS6uMhX0MUJfm++rKmxPYLrv9MUVJ91LtQLyQk31ffw5RUHye0 mWKRVB/X1X++KLH7c7UnvympPhZue9iR2PmEXpyfkOpjWy/WSkj1MWe73xFJ9TGEDe7rR5LnRY9l SqqPBT1sO1Ni+336mqcoqT7u97CfElJ9/ORhzySk+pjKi0sTUn2s52HrmBJ7/8WLexNSffyuDM6/ RJLn8b1vSqqP2ht4gqKk+njew75MSO4/NmJRkveztzcl1ccNvoYsSuz+ixc7JcT+fPGwcU1J9bGR FxslpPoY14urEmI/r3vYeaak+tiu9aSLJJ8P+sCU5M8foxYl1UftPT99UVJ91LsdYxYl+f3HV6ak +pilzc+KpPqovaPfT4jtT9fOFEZSfUzkYSeZsp8P1M8Hqj7u8PWOKbHzs9tMwkjs/Upf35gSe5+w 3S+NJN9Xvy4h1cfsHnagKbH9LjzsKlNSfczUnmkjyfPmX0hI9VF7Sc1RlNjzuL7GLkpyf9yLTEl+ XzhdUWLvZ3vYzwmpPm5t+y2RVB/vetirCak+vvN1tSmpPrb3YvWEVB919s2ZpqT62Lrt50dSfWzo a/6ixPaj9+KAhFQf13vYhKbE3gfysEtNSfWxl4etYEqqj6fqZzJTUn3c1u4fR1J9POFhnyXE3kf2 sJVNSfVxbtuvjcTOw2nP95HY/jAetq8pyfvZo5uS6mM2L45LiL3v0c7ARFJ91NmdN5mS6uNED5vD lFQfo9pgzyWS6mNSL65IiN3f92LNhFQfU7f7cpFUH4t62BamJJ+n29WUVB+X+/rWlFQfc7Q7c5FU H0t6sU9CbP8PL3ZLSO5nsGlCqo8666UUJdXHxG1GQSR2foOHjW1Kqo86y2NLU2I/n3pxYkKqj7M8 7E+mpPqos38PMCXVx48e9mBCqo97POyHhFQf87aeQZFUH1972OMJqT6W97B/mBJ7vrB9D43Ezgfy 4v6E2P7aHvYvU1J91Lulz5uSfB5mH1OS5zc8nJDq42xfExUl1cffPWxPU5LnJU1nSnL/oPFMSfWx RTfocRFJPl94bEKqj0c97IuEVB/1LNBcRUmeH3V+QqqPy7rBvIZI8n7DRKbE3kf2YpOEVB+7eNgS pqT6ONXXWEVJ9XFY+zwaie3X58V/EpLnndyYkNyfbtaipPq4xcOGMyXVx4rtfGUk1UftBXNUQqqP wz1sRlOSz1tem5Dqo/ae/zYh1cdq7b5LJNXHwW1mQyTVx2JeHJ6Q6uMP7Z1YJPY+UJt3G4k9v+7F ngmx919av49Iqo+TPWwKU1J9XNfOwESS33/MXJRUH0N48UhC7P6th+1kSqqPTTxsY1NSfQzrYfeZ kurj/vbzJJLqo/Y+mdWUVB8LenFkwr5/UN8/qPrY1ou1EpLnAb+XkOpjmvYMF0n18bKHvZOQ/Pxy T0LsfMJ2hi6S6uMgX1MXJdXH0u1+WCT5PtAWpqT62NTyRfUxYhnMVI+k+vjZw55OSPWxg4etY0ry fY8LE5Lfn65uSqqP2ttz0qKk+qh3bY8wJfb8qYetZ0qqjw9bj4tIqo83fD1oSvL59aFNSfXxlYc9 l5DqY7wy6DEeSfVR75YeZ0qqjys9bAxTUn0M7cXdCak+ru4GPdgiyf36hilKqo9RvLgtYX8/qr8f 9Vt//h9MSfVxSfv5Gkk+LzWuKbF/PrrBL0RSfUzWHESS+7HNXpTY+ci+HjAl1cdNrX9BJLYffTtv Gkn1camHTWpKqo8ZvDgjIdXHUx72fULy/Nt/J8Sed/A1d1GSz9NtY0ry+7FPTEn1Ue8eH2ZK7H6l rw9MSfXxioe9n5Dq49g2by6S6qPexa53PCKx/dc97EBTUn0s3OarRVJ91F4Opyckzys4OSHVR+3N N2xRUn0M72G3mpLqY8I2IzqS6uMZD/syIdXHgW3GWiS5X85qpqT62KDNa4ik+ljd8kX1cYKHTWlK qo/XfT1nSuy813beNJJ8XmosU1J9rOLFjgmx5y19TVmU5PMfY5iS6uNpD/shIdXH+x72ZkKqj889 7JWEVB8bdYN5QJFUH7e1r5FIqo8h22ewSKqP17rB/eNIqo/lvNg9IXZ+gxf7JKT6WKSdj4qk+ljX iy0TUn38xYsTElJ9POZh3ySk+hjOi3sTUn083AIjqT62a2ccIqk+Lmr7C5HY/uvtjFQk+fvprQmp PlbysLVMSfVxs4cNZUqqj+faGZhIqo86u3NtU1J97NKeaSOpPrb2Yu2EVB/1LtSzCak+XvL1hCmx /S7afJNIqo89PWxRU5L7w4xalFQfI3lxZ0Kqj3pW7E1TkufPHZyQ6uNVD3srIdXHom3eSyTVx12+ 3jEl+fzYxwn790H9+6DqY3IvLkiI3b/1sENMSfVR7x6PXpRUH5t52HKmJJ8/fT4h+X72UEXZvz/t 359WH/Xsyw2mpPqoZ1++MyXVx1JtTz+S6qPOJngiIdXHg81BJNVHnVX5D1NSfVzj62tTUn0c4Wu6 oiTPN70yIdXHAl4clZDqo+61fJ2Q6uOz9jwbif168bDdTEn1caiHzWRKqo/RPewcU2LnR7X+BZFU H8e3friR5P4wE5oS24+t/jsUJdVHfddR+4tHUn3U3jiXJSTPv53ClFQfH7XzQJFUH5962DMJyT9f 5i1Kqo/6bH+PKcnPL/8yZX9frL8vVn3s3N55RFJ9XNa+RiKpPub0sF1NSfWxRrtPGUn1sb4XmyWk +qhnK2cxJdXH2x72UUKqjyFaf5xI8vePzRNi7ze092GRVB9HetjcpiSfP10nIdVH3YubwZRUHxv6 mr0oqT7eqWdyTUn1sYeHzWtK8vnTN0xJ/v4xZ1GS348takqqj7G9uC4h1cft3eB+RyTVx0keNrMp qT5e8LBPE1J9nO9hU5uS6mMZL/ZOSP7+Ma0pyf1hPkxI9VFnE6xoSqqP/VtPh0js5zEPK6ak+tiv /npRku9nv21Kqo+XfT1lSqqPgz1sdlOS+219lZDcj+1LU1J91LPZx5iS6mMML25OSD6Pe58pyfez D09I9XGeh01gSqoP87CrLGHHvZ+9rSmx/WF8zV2UVB8ftGeWSKqPHTxsQVNSfcznYTuZkurjwPZ+ MJLq42hfvy9K8vP+1wmpPmZs74AiseelPOy7hFQfI3rYFaak+qi9Ps42JdXH9TWvKKk+VmzzPCKp PhZve3KRvY/eR/Vxi4cNaUqqjyfb+blIqo+/etjGpqT6uKkb9LSMpPr4st0hjKT6WN6L3RJSfRzj a7yipPpYxYsdE2L7Bft6xJRUHzd62GimJJ8/ndeU5PN0z5uS6mM9D/ubKak+XvH1sCmpPlZqP18j qT7e8HW/Kak+VvOwNU1J9bF7N5hxEkn1cXI7cxpJ9TGZhx1nSmz/wvZMG0n1sWDr3xhJvk+4tCmp Pn7ysEcSUn3Udx0/JcTOA/awMU2J7ZfT5mVHUn2s68UWCak+hms9LiKpPh7z9ZIpqT6292L1hFQf T3WDfvyRVB+3dYM7DZHY+w2+/liUVB91ducTpqT6eLZ9v4jE9jOo74SKkvw+eRNTUn3U3msnmJLc L2eaoqT6mLW9H4wk9z+9MiF2nkWb8RqJfb/efsZGkt+vL2pKcj+U60xJ9bG2r3mKErt/68WFCcn3 b/czJfZ9oa8ZihJ7HtfXD6Yk9x+7MSHVx8bdoD9OJNXHyl7slJDcb+taSwj1cYeHDWNKqo9tvVgr IdXHqh62lynJn9cvTkj1sZSHHW5Kqo8rPWwiU1J9LNneh0VSfZxQ92CKEnv/pc2HjqT6eMjDhjYl 1cfdbY8hkupjUy82SEj1cVH9Z4qS/HlsM1NSffzo61ZTUn2s6cV2Cak+lm5nPiKpPg7zNW1RUn3U 2QQXmhLbb8vDxjEl1cd4rcdnJNXHxB52sSmxP299zVGUVB/zenFkwr4/Xd+frvoYpe1fR5K/f8xZ lFQfT3SD+4ORVB/ftDuVkVQfb/l63JTk+0CTFyX2PlC7QxhJ7q/9XULy/IYhipLq42FfH5mS6mMT LzZKSJ6nNW5RYu8Ttplzkdh5fG3ebSTVx+O+XjQleX7UCaYk71deY0qqj5E97BxTUn3c7+tNU1J9 TOnFBQmpPtZoPdcjqT528bAlTUn1sULbX4gk93e4LiHVx+hlMEMrkurj+7bHEIm9T+hhG5mS6mMs L65JSJ7nuX9Cqo9ZPGxvU1J9bOVhS5iS6mM7D1vYlNj3Yx72ZUKqj9eag0iqj6vaGYdIqo8L2/nb SOz9KA9bwZTYeWut32kk1Ud9VlnFlFQfn/i6z5TYfvQe9kVC8nn+k01J9XGsh01nSqqPOtvk96ak +njfw15MSPWxebuDHNm//+jff1Qfl9YzD6ak+viXh41hSmw/WC9OT9ifp+vP01Ufc7czp5FUH/t6 2DympPpY34vNElJ9LNDmeURi+9N52NampPo4ohuc34+k+jig/p6LEvv84sW6Ccnnpa5JSPVxgYeN a0qqj5d9PWZKqo/ae36aoqT6GKq+8zAl1Uf97LW4Kak+rvX1lSmpPnb2sEVMSfXxdw/b0JRUHw/6 eseUVB+199p4psT2l2p7lJFUH/O0/muR5O+n65iS6uN1D3sjIdVHnd05vCn7+YT9fMLq4xkP+zgh 1ccHvu4yJXYecLs/GEn18a6ve01J9VHPEh5iSqqPdbzYMiHVx1+92DMh1cfsXhyXkOrjd17cmpC8 fztxUWL75XjYoaak+qhn1Y83JdXHO91gxlok1cdt9TOqKak+PusGM18iqT4Wa/OiIrHnLdt920js +zEPW8iU5H6O55sSex/Z16xFSZ5vumFC8nzktxJSfczmxfEJqT529LBFTUn1MVKbFxVJ9VHaecJI qo+/eNhupqT6OLP1XI/Evl9v5+cisftzHvZKQqqPp9t+fmR/36O/79F/P036jXvYBqak+nixnQmK pPq43cOGNiXVx8m+Ri1Kqo/52zNtJPZ5vxvMzI6k+ti2G8xTj6T6eNbDvk1I9fFpO68eSe7Pf2BC qo9LfE1QlFQfdRbQ3EWJvZ/txd0JqT4+bj3oI8n3545LSPVxXze4bxtJnp/9himx8yw87M2EVB9/ 9uKkhFQfy3ixV0Ly57HZi5Lq42YPG9WUVB9rtXcekVQfP/l60JRUH7XXx1mmpPrYoPV/jaT6uL49 00ZSffzJi1MTYu/PedjcpqT6eMHXk6ak+nirvf+JpPrY2MOWMyXVx7xtPkEk+f3pcwmpPupZwudM SfVxrq8RixL7/rT+WTAldj6yrw9NSfVRe42dlZDqY4S2PxmJPa/dDc6sR5Lnm36bkOrjEF9TFmW/ /9Lvv/x2H3mDhOT7yP9NSPXxnq87TYmdH+VhM5iSPN/0J1NSfdzh6wNTkvuhXGRKqo/7PeyXhNj9 Bg/7NCG5//pIpqT6+N7Xbaak+viwfc+IJO+/HJmQ3I9tMVNi3yd72BcJqT7W7gZn+COpPq729aUp qT5W9mKHhOTzME+YkurjhG5wXz+S6uOT+sxvSqqPUz1sKlNSfWzjxVoJyV8vd5kS++ejncGNpPo4 rc1siKT6eL4uU2L7sfkasijJ/baeMCXVx/7doL9FJNXHV75uMCXVx6P1a8aU2PnZbb82EtvP0Ytd E1J9bOnFugmx/T887MeE5Pu3p5iS6qP2thilKLHzotvP10iqjz3a+dtIqo+p2hm6SOy8Vw/b05RU H0+27xeR2Pu3bYZWJNVH7d14REKqj+XaTMJIqo961nRMU5I/f0xelFQfK3nY2qak+njEw75OiJ2P 7GFDmhLbD9bDdjIl1ccuvqYpSnL/sU0TYvdfPOyphFQfb3eDfoWRVB+P+XrFlFQfu7efKZFUHw+2 /gWR2PMwHvZ+wn4ecD8P+Nf5QN2gX2Ekeb7pywmpPvbzsFlNSZ4/t50pyfOz9zQl1cckHna0Kcnz +GYsSvJ8sa4oqT7G9+LfCcnP+/ebEvs85+t1U1J91P+dnRJiv1487NWE5PlRJyak+qifNU5JSPVR e7/WHn2RVB9/87B1TUn1Uc/uT1WUVB9Te9ghpsT2T253kCOpPj5qd0wjqT72rblFSfVRe88PU5Tk z2OnJuz7XfT9LqqPJ7rBefVIqo9z2h2xSKqP0by4LiHVx7gedqIpseeDWr/CSKqPazxsBFNSfXzW zhNGkvt9fp6Q6mMRLw5MSD6P+0RC8ufT50xJntf4uCmpPibz4qKEVB+jt8/nkf15qf68VPUxeTsD E0n1MWXrARtJ9TGLF6cnJN8X2ywh1cdCXhyckDxP/K2EVB+rebFjQqqPelZ9WVOSn/cPSUj1cWT7 TBpJ9fGAh32XsH+/3r9frz7Ob3sukVQf03lxZkKqj8s8bAxTYvez2/mXSKqPoT3sFlNSfdS7DH8p SqqPa9vPk0iqj9k8bH9TUn2s4cU/E1J9bN7O8EdSfVzpYROaEnvesr3viKT6WMbDNjYl1cfJvkYu SqqPZb3YPSG5P+5YpqT6eMvDXk9I9XF627ONpPoY3sOuMyX2vHY7/xJJ9VFnzV2VkOqjvkt/2JRU H6u0/dpIqo+t6zuQoqT6OMjD5jMled782EWJnY/sa8SipPqo3zunKUqqjztaYCR2Ho4XuyWk+viv h72RsO/P3/fn/3Xeq6+Zi5LqY/1uMFMsEnt+ve1PRlJ9HNAN7kRFkvuNv56Q3M/gTFNSfVzoYROY Ervf4OtRU/b3K/v7ldXHoh62pSmx98U8bHlTYucBe9hfTUl+3t89Iba/g4d9lpDqY6/2+TyS6uP/ ae88wLWqjka9Z9tALBh7L9FI7L0XiMaa2I1GRUFRBFFBEOxiNPbeW2yx95poxIYFa9TYe/mNvYAS K+qdxZ6TkJmx/Cn38d538zwrL3OAM543+9ttrTVzu453JJLq4/Oqmc/3JPcnfEkisfcfOlasI6k+ NrLrqyfVxyh75+FJ9XFX+dklkupjW3un7kn1cYYmm1ciqT5Os/WVnlQfu+hYoo6k+jhUky0lkVQf 89ueW09sPy3r9+JJ9TG8amqweVJ9lGf75xO2/SzafhbFh9ieykCoj2E6FqkjyfuRN5BIqo+bdHwk kdj9+5IP7P4GDXolJNc/PSUh+fOypURSfTyk43mJpPq4UpNNI5HkeuP7SiTVx3b2jO9J9dHH6kd7 kuuPLVBHtvMv7fxLR32HuSWS6mNdTbaLRFJ9LKzB2QmpPspehj9LJNXH1To+k0iqjz9psskkkurj fOvv6kn1MY1dYz2pPjppcFtCqo+bNdkkEkn1sYW9E/PE7je1Pbee5HpKQxNSfSyuyQ6USPL6saXq SKqPUuvjQYmk+nihanq+eFJ9/KZq9kN5kvtZXCaR2P5zmmxriSTXg71IIqk+yrP9SRJJ9fGMXU88 yeePrSSS6mMRq+HoSa6//nJCcv2x5etIbL2+suZSIqk+Xtdxj0SS+yMPSUj1cYOOsRJJ7re2v0RS fayqyfaQSPL7j3nqSKqPxTQ4MyHVxwoaHJ+Q6uNrTXZvQqqPgfYZ8aT6WFKD0xJSfTynyd5KiK33 aetfPMn16eapI8nzlfdJJHY/siZbXSKpPq7S8alEYp/nNDg6IdXHPtY/y5Pq47EyJyWR5PWWk0kk 1cdammwviST3r3xJIqk+dtegZ0Kqjx72/seT6uMITbaORGLrr1dNjS1Pqo++tt7Dk+rj9PIz15FU H7NocH1Cqo9jrOeLJ9XHnXb+9KT6WE2DIxJSfXTR4JaE5P3qD0gktt+J7af0xNZT0uCMhNh6jrYn 25Pqo+wNqyWSvN7hkYRUH6dosmUlkuqj1D55IiHVR6nl8LlEUn3016BvQmy9HB2T1pFUHyeXv1tH YvtZWM1CT6qPjTXYOyH5eU4kEvu8bz3EPak+VtFkB0kk1cfmdv70pPp4UccLEkn1Mb0mu1AiqT5K b5PdJJI8v7+SRFJ9TG31PjypPmavmxqwnuT9c2cnpPqYUYPrElJ9XGF7Xjyx9Qw02UsJsf2Ay9fq SPJ6umclkurjQ5tf8KT6WM/27HtSfeykwQ4JqT4m1mBUQqqPWoP7ElJ9TKTJrpNIqo9F7Rnfk+rj VE22oERSfYwtc/wSSe6ffZUkhPq4uGq+4Imdr9TxlkRSffxRk3WWSKqPJzXZewmpPh6x+TjPtl9B 26+g+Ohd5vjrSPL7oCcTYucbNNnZEkn10UuDQQmpPrapmho5ntj6HxockpDqY1dNtp5EkteP7ZGQ 6uMtuwfzpPq4VMc4iaT6uMDed3hi56Ps/OmJvb7oWLyObPtnt/2zi4+jNdliEkn1UWrBfCyRVB9b a7BbQnI/4GEJqT7O02RzSiTVxw6abFOJpPrYUYN+CbHz2VYT15Pqo58GOyak+viZ1dfypPqYyvbs e2L7rWmyLhJJ9XG23W94Un2coMkWkEhyva1OEknuZ/GZRFJ9TGH1Gz3J+8Wml0jyfPbAhFQfD+t4 USKx60812cwSSe4f9XOJJNe3/CQh1Ue5tpZ62p5UHztrsl9IJNXHy1VTP9qTvH/u7oRUH0tpcGpC qo9RmuyLhFQfG2mwb0Kqj0s02UwS2T7vt8/7xcd7muyZhFQfd2uyrxJSfSyowbkJyf3FNpZI7P4G TfZriaT6mFuTHSeRVB9r2J4GT6qP0qtygERSfZReptPUkeT1UjsmJN+vj0hI9VHmnpaoI7Hvx2yO 0pPqo7J6Y55UH6X2/AJ1JNXH82UOVyKpPg7RZMtIJHZ+X5P9LSHVx/wanJ+Q6uNYHdPVkVQfz2my txJSfRxcNTX5Pak+FtJkB0sktn6Qjpslsl3P367nLz420WTbSSTVx8zW89YT209ck+0nkVQfv7M5 Bk+qjw1tvYcnuX9lLZHk/Q3TSSS53+s+Ccn1DGaXSGz9D022hURSfZS1+3dKJNXHYZrslxJJ9XGb 1YD1pPp4W5P9T0JsvxMNfp+Q3O9kOYmk+rjDegJ5Un08ZD1OPKk+fqLBRQnJ/bN3lEjsfnUdS9eR VB+lN+N8dSS5v+nTEkn18YXNwXhSfWwr+aD6mMPuST2x9U812W4SSfUxlya7QCLJ87cDJZI83zC7 RGLX82uyiySS6qPsZSj9KzzJz/ufJyTXM9gvIXn92AiJpPoo915rSiTVR38N+iak+hijyZ5ISK6H MotEYufnyjshiSSv/5hfIqk+trD+Jp7k/tljE1J9DLKeyJ7Y+Qa7//IkX19GSSTVx2DrAexJ7u8x IiHVxy6abF2JbOtLtfWlio8eGhyZkOpjiNUX92z7Rbf9ojv2v0wkkdh6F+VnriOpPk7UMX0dSfUx owY3JCQfHzPWkVQfm2qwd0Kqj0k1uDMhtn6hJvuVRJLPp9cnJM/vf5yQ6uNMHZ3rSGy9cU12qERS fexUNT1OPKk+VtVkQyWS3F/s04TY9Q5Vs+fWk+rjOk3WVSKpPvawGvSeVB+ll/pHEtl+XtrPy/jP i46F60iqj6Wt35wn1cefrQaKJ9XHVhoMTkjeL7a1RFJ9lN57p0kk1cdwTbaiRFJ9lLWEf5JI7Pyt zWF7Un2UvWEPJqT62FyT9ZZIqo9drf6aJ9XHnJrsJImk+jhcky0tkeT6lltJJNXHgTrmqSOx+4Fs Tt8Tu//W9g96Un2UXg3nSyS2n0XV7DH1pPpYyeYYPKk+ntJk7ybE7m/QYFBCqo+RltCT3B/5R3Uk +XnuRImk+thfk60ikeT1uCMTUn1cXDVf8KT6mNLuzz2pPna3/eme2PrJ1lPdk+pjlNXE9cT2A9Zk R0gk1cdB5Z6sjqT6KHuxZ6gjsev5NTgnIdXHxJrsUomk+lhNg8MTYvvhlHvUOpLqYy8d3epI8vPc 1xJJruc4o0RSfVypyaaVSKqP6+0Z35Pq45caHJAQu39OxwsSSfVxmSabXiKpPh6w48GT6qP0hv5J HUn1cYwmW1giqT7eq5r9tp5UH6VXw7x1JLkf8HMJsf3WNNglIdXHpXa/4Umub7mmRFJ9rGBrYDyp Pj7TZH9OiH1+qZo9UZ5UH9NbvTFP7PlUxyJ1JNVH2QvVTSKx7wurZk+DZzt/287fFh+fa7KHEpLr GZwqkVQfJ5RcdSTVx+LWA8eT6mMdTTZAIqk+ptXgjwmpPn6kyc6WSOx6XB0r15FUH6WXxyMSSa4v lfUIwtZf16BfQvL6jykkkupjSU12hkRSfZRa6w8kpPq4wO7RPcnrte+VSKqP3rYfypPqYwMNhiek +lhOg5MTUn08q8lGJyS/DzpcIqk+7qiaepaeVB87WI8TT6qPs6zGhSfVx106XpNIcv2xCySSPJ+9 kERSfSyhwdkJqT7e0WSvJaT6uM36m3hSfQyyesmeVB9lb9jCdSS5/tgpEol9H2TzLZ7k6+0ZCcnz 2edJJPn92IkJqT7ut35RnlQfG9ueSk+qj0U12YESiX2+1TF7HUn1cVHV1MfxxPbjs2daT6qP0lv+ bomk+uirY5U6kupjX3ue9aT6+KOtj/LE1qOvmv4Vntj+USVvHUn1MUCDHRJSfZR70SsTUn2Ua+sx Cak+1rP1UZ7k+jDz1JHk/XPT1pFUHz/RZMdKJNXH9hoMSEj18ZWO6ySSvN9jKomk+ii91PeVSGx9 fk22lERSfZS1QJ3rSKqPGzXZ5BJJ9VHe/VwokeT5yk8Ttv3W2n5rxcczOh6VSKqPQ6y/vCfVx+/s +uqJPZ/qeFUisfcfOj6SSOz5o2r6iXlSfWyoyfpJJNXHz6xnpSfVx6802XYSid1fqckmkkiqj5U0 OC4htl6OJttYIsnzt1ckpPrYzurxe1J9zKjBtQmpPo4yB55UH8Nt/toTu3+//Ps6EtsvWpMtL5FU H6fomLqOpProY88snlQf52iyuSSS6mPnOifVxx5VU5Pfk+pjVg2uSkj1cXT5u3Uk1Uc5dx4nkdh+ FrZmyhP7/GJrpDypPrbRYFBC8nrLqySSPN/QWyKpPo6z/r+eVB+lltS5EknuN/+SRJL74ewikVQf h+mYrY6k+jjUfn5P7PVWg70SUn1srsGwhNj1MBockZDcD/gLicTun6uammOeVB/zaLJjJBJ7vbX9 UJ5UH6N0vCKRVB9l7dxlEkn1sb8mW1kiqT7GSdM/yxPbP6puehR4Un3spsnWlkiqj5+bA09yva03 JZLq43xNNptEUn1srWPVOpLq40+abDKJpPq4WJPNIJHkekpd60iqjz/oGC2RVB8f6bhJIqk+TtNk 80pku9+j3e/R0Y9vLomk+phBg+sTku9PV6kjyfXon5dIqo/lrd+LJ3l/tkgk1ceqmmyoRFJ9lN6M 90oktn+lfWY8qT5e0GSvJ6T6mN7uvzzJ/Qk3k0jyfNSdCak+7rQ1/J7k/mJT1ZFUH6WX2M0JqT5K L+T+Eon1YT2RPbH1UDTZYhKJrQdr9+ieVB+rW091T6qPUlvrU4mk+jhdx+R1JLke7PsSSfVRauPc nZDqYx+rV+hJ9fFTW7/vSfWxsj3DeVJ9/FbH0nUk1cd9Ov4mkVQfJRiVkOpjSU12oERSffTUZFtK JHn9aSeJpPo42PqbeFJ9bKHB0ITY9fwlXx1J9bF31fTz8CTXY3tQIqk+xup4RCKpPraVfFB9zFc3 NR08qT420WCfhNj9phr0Skj1Mdp6EnpSfZTeWZtIJNXHizoek0iqjzd0PCCRVB9L2JycJ7YevSZb VyKpPm7X8ZZEYvd7aLK9JJLqo6z12Egiyf1v35TI9n69vV8vPnatmj1inlQffTXon5DcX30ZicTO 79s11hO7XkqTXSKRVB9TaLIedST5fv0diaT6eLWsiZFIqo83q2ZPlCfVx0CrV+iJ7Q+kyTaXSKqP e8o7Q4mk+ihrG+7LCPWxgAa/T4h93rd3yJ7YeuO2/9iT6uMGe2bxJK/XfkUisf34zIEn1Uc3TXa0 RGLfF9r8gie2HqwmW0AiqT5m0WSnSCTVx04a7JCQ6uNwTba4RFJ93KLjXYkk71efso7E7n8peetI qo9OGtyRkOrjOnt+86T6WFCDcxOS9zdsJpHYerAaHJMQ+zxn6188qT6erpr12Z5UH0OtppQn1cdm GuyRkOqj1ML9UCKpPl63PR6eVB8XaLKZJbLtL9b2F+uoj9u1jqT6mFuDSxOS+81/JZFUH2Vt1K4S Sb7evpyQ6uNS68/oSfUxrwYXJaT6ONv6q3li9wPZ/lJPqo/DrCadJ9XHMHuH7Emej5q9jqT6KGtN 6zqSXC/4cImk+riqaurPe1J9jLD1DZ5UH+tpMDwh9vnFnu89qT6W1eDkhFQfV+r4XCKx6ws12QYS SfVxjY6PJZLqYxdN9guJJNeHeUkiyfX61pdIqo/tNdgpIdXHzBpcnRC73lLHRxJJ9fHXqtlT6Un1 0d3WSHlSfWxte5A9qT66aLILJZLq41Edz0ok1cdrVVMfx5Pqo789z3qS9+9PIZFUH7NpspMkEtvv RJM9mBD7PGf9Oz2xn5e6eWfqSfVxkSabUSKpPtaymuueVB9l78/ohFQft2qyiSSS6uMpTfZeQqqP STS4MyHVx5N2PHhSfXyh43qJpPpYUYPjElJ9bKfJfiWR2P2V9nzvSfUxUpN9nZDq41pNNpVEYuvB arJDJRJbn79u1lh6Un38RZONSUj1cbwmW1AiqT7u1mTjElJ9HFg19cY8qT4Oqpp+6p7YesE6rpZI qo8rdHwmkW19qba+VEe9nI8kkupjiCZbQyKpPi7U8bVEUn0spcn2l0iqj+E65qkjqT6e02RvJ6T6 2NH6d3pSfbxczhUSiT0+NNkBEoldT6djujqS6mMGDf6UkOpjKntf6om9/7D1QJ5UHw/ZmlNPcv3k lySS6qP03jsjIdVHT+uf5Un1Ud6lX5+Q6uM2TdZJIqk+LrHriSfWh92DeVJ9rKbJDpFIqo/F6uad qSfVx+NVU//Ek+qj7C39LCF5vmHaOhK730PHqxJJ9VF6V7wokVQfR2qyHhJJ9VHWZveWSPL79WES SfUxRpM9lRDb70ST/Vwises/dCxSR2I/Lzrul0jy/O0bCak+zrP7c0+qj2lKz2yJxPYXq5r+WZ5U H3PanjlPqo+fWb9bT6qP8tO+LpFUHzdpsnklktxPaxmJpPrYRJMdIZFUH6XXy0MJqT62Kf8NdSTV x5c6rpNIcv+obnUktt+rJjtDIqk+yrFwfkKqj+fLmjqJpPpYQZOdJZFUH7/U4DcJyfsJN5dI7OdF g1MTYtfDaLJJJBJbr0+T/VkiqT7+rGOcRFJ9XK7J5pNIqo8yV3uiRGLr9VVNPQdPbL0Lqy/uie1P qMEOCbH1k3V8IJHk+blTJBL7/KLB1gmpPma1fnOeVB+H2fooT6qPNay+pyfVx+1WH9iTXG9rsjqS 6uNiHbPUkVQfD+j4VCKpPkqtsScSUn1spcm2lEhy/bF560hsf2Sbf/Kk+rjFnmc9qT4mr5tnfE9s PxwdPepIqo8BOpauI6k+VtHgxITY+jCa7BqJxNaH0dG5jqT6KL0aLpZIqo/TNNlKEkn1UX720yWS fD/2YEKqj01tv74n1cc7VdNTzJPq41gd09eRVB+lt0lXiaT6KHuP/5CQ6qOsVZ+5jiQ/v5wqkVQf Jbg/IbaeUtX0r/Ck+phak10mkdjnFw1OSEheL3WlRFJ9lHNnWZ/tSa43fl5CbH1cDQ5PSN6PfK1E ktcXXpWQ6uMiHV9JJNVHuRe9NCHVxyea7JGEVB/lXemvJZLqYw7roeVJPn9ckpDq49OyBkQiqT5O 0bFAHUn1UWrRLVJHUn3sYGtgPLH75zTZDBJJ9bGuBgcmpPootbWmlEiqj3HmxJPqY2MN9klI9bGM 3XN4Un0Ms5oOnlQfH2qyZxJSfYyy/uGeVB9lb/qqdSS5Hv3ZEkn10d+eVzzJ608fSEhezz9lHUne /3JyQqqPXppsM4mk+ihzLc9IJNVHJw3uSEj1Ue415pBIqo/preaHJ9XH76zGuCe5X9K7Ekn1Udbu V3Ukef3pcQmpPsra2xnrSKqP8Wsb6kjs+mSrz+eJ7a+uyRaVSKqPu6um/ponuV7w5hJJ9bGlBkMT Un1cWTU12DypPibVZC9IJNVHV6sn5UmuB3uKRGL7A2myIyWS6uMeTTatRFJ9vFo1a/g9sevHqma/ vifVx2U2H+dJ9TGFBrcnpPr4se2X86T6eLM840okef3pHySS/D75+ITY98mabBGJxPbj0+DehFQf e2uybSWS6mMdDQ5JSPXxiib7LCHVRz9bM+ZJ9VHWih0okeR6jgvVkVQfj+l4RyKpPsqxcG5Cqo+J NdlNEkn1cZwmW1EiqT7G2jnDk7zeYWaJpPp4S8dDEkn1sZsmW18isdcXDe5LSPVxc9XsifKk+phN k50rkeT6QaMkkuqjtvOFJ/l+/R6JJNfreyIh1cfSmuwIiSTv3+9RR1J9lFrJnepIqo+vqqY+sCf5 87JyHUnut/YTiSTPN+wgkdj6dJpskERSfYzfe1xHkvtH3ZaQ6mNl21PpSfUxlQZ3JaT6mNH2ZHtS faxo9Qo9qT5W12SHSyTVx8IanJ2Q6mN/TbamRFJ9bGP7bT2pPjawPcieVB8Pa7KxCcnvP7rXkVQf L2qy1xNSfexp9ZI9qT5esjUfnuT9Uc9LJLkeyucSSfXxdNXUX/Mk1zM4RCLJ9RxHJKT6KHvlTpdI cv+56xJi68NosnMkkupjH022ikRi3yfb+cKT6uNA28/gSfVRnmXvk0hyP5wnE1J9zFc3PaI9qT5m 0OCPCcnX2zUlEtvvRJN1kkiqj7U0OCwh1UfpHb6TRFJ9jNExUiKpPkptrc51JNXHjXb+9KT6eKPU w01I9XF51eyJ8sTON2iyLxNSfRxt9+ie5P6V50gk1cd6mmygRFJ9XKHJppdIqo+NNNgvIdXHvFYT xpPq42IdP6ojyf0sutSRVB+H2vyCJ9VHT7u+elJ9PKvjUYkk7xf7Q0Kqj962x9ST6qP0argmIdVH 6S1fauJ6kvt7TFRHUn0cpcmWlUiqjyltPaEn1cdQTba2RFJ93G/1xT3J19vrE1J9LGs9LDyx11ur WehJ9XGyJltCIrHrLXXMXkdSfZS1YmMkkuqjrBXbWSKx/ZE12VYSSfVR3v38TSKpPkov9TsTUn3s bD1vPak+DqqaNdqeVB/b2jnUk+rjJE32U4mk+ljU6gV5Un18rckeSUj1UWqdnieRVB/l3eABEkn1 MUCD7RNSfTyq4xmJpPqY2tZXepLrnx6bkOqj7HX5OiHVx+802dwSSfVxviabVSLJ9elWqSOpPj6w 9WKeVB8DdSxVR1J9DC5zlnUk1Ud/DfompPpYxtYke1J93KvJJpVI8n6x30tkuz+q3R/V0X/upYRU H+Psfaknub/pnRKJrb9ua2A8sesdNNgzIbn/y40JqT521GR7SCTVR6nl8JREYt9/aLJXE1J9jNZk zySk+rhEk80nkVQfH+u4WSLJ/SxWl0hy/6iNJRLbH9n2VHpSfdyhY+I6kupjmO3J9qT6WN9qwHpS faygwckJsfXYNNk6Ekn1sbsGPRNSfVymY7o6kuqj9A5/OCPUx+Ya7JGQ6uMYHfPWkVQf69r7dE+q j7012aoSSfWxhSbrJ5FUHxdpspkkkupjVqtv4Ynt32D9CD2pPkqv28MlkurjSVuv7kn10VmT3SWR VB8f2fykJ9XHj+ydqSfVx0IaXJCQ6qP0Dn9OIsn7o8r6W0+qjxM12aISSa4PM1YiqT5O1WTzSyS5 f/bhEomtd2HPb55UH7freE8iyfv3X5dIqo+3q2Y/pSfVxxea7C8JqT6m0mBkQvL+7JXrSGy/V5uf 9KT62MNqfHqS70+Pl0js+9O6uQfzxL4v1GRnSSTVx9y2JsiT3N9jcYnEPs9psokkkurjAqsX5Emu f7qERJL7i+0okVQfl1ZNv0pPbH1tq2fpSfXxro7HJZLq4zRNtqBEYuuNa7BrQnJ/sQ0lkurjBqsB 60n1cZ8m+zQh1UdXDW5KSPVxhCZbSiLJ/aIfk0hyfe0edSTVRz8NdkxI9TGDvS/1pPoovcP7SyTV xwIaXJSQ6qP0InwuIdVHqX0yRCKpPjaxHmue5PqFwxJi68NossklkupjOQ1OSojdP6fBoQmpPnpa P0JPbP1CHbdKJNXHmZpsXomk+ii9bt+SSPJ+5CESSe6XNKdEUn0caesbPMnrk3vUkVQf3TXZbyWS 6mMjO396kvsBP5yQ6uP+qqmp7Un10UmTXSiRbb/Gtl9j8VFqae8mkVQfZe3cCnUkth+fjiXrSKqP UmvsY4mk+pjD1mh7Ys8fGuyckOpjPQ0OSEj1sZeORepIqo/dqqbfrSfVx9Ka7BiJxO7PtvqvnlQf n1dNjS1Pqo9VrKa2J9XH8ba/w5Pq4zzraeqJrS+lwZkJsecPq3HhSfXRR4MBCak+ZtfgioTYfkma bF+JpPoo78JOT0j1MUrHmxJJrr/+YULsfJQGdyWk+hikQa+EVB/PaLKxCdv9Yu1+seLjMVtz6kl+ vz48IdVH6f37skRi1wfpuEoiqT4u12TTSiS2fpAm+4VEYuej7P7Lk7yfcDuJpPq4VpN1lUiqj/k0 uDgh1ccfdYyTSPL7j78lxD7vV80eU0+qj9LL44WEVB+zWE8gz3Y/ULsfqPjYQZP9SiKpPm7WZHNJ JNXH7zXZshJJ9XGY1YTxpPo4V8c8dSTVx5W2PsqTvN7h+oRUH2WuZeU6ElvPUYObE1J99NVkm0ok 1ccA2zPnSfUxXJOtLJFUHz/RZCdLJPl94ecSSfWxmiY7WCKx9+uabDGJxB4ftr/Dk1zPYEGJpPq4 pWq+4En18bAm+zIh1cfzOt6WSGw/i1LDQCKx9eg1uCEh1cd1VdND3JPqQzS4NyPUx0LW88WT6mOI rZ/zpPp4VcfTEkn18Zkm+0tC7P2Yrd/3xNbnt+urJ9XHgZpsLYkkzzf0kkiqj99osnUlkuqjlwYD E5L3A70qkeTr7bsJyev5p5ZIqo8zdExVR5LXjy0lkdj3QZpsGomk+thbx4J1JNXHVLan0pPq47e2 3sOT6mPXqqnv6Un1sX/V9DT1JNcbX7GOJPebvzUh1ccLmuz9hNjzqSZbXyKpPk6wOVtPqo9p62ZN oSfVx9waXJIQO5+tya6QhNT1H5rsDInE9p/T4KiE5Pp07yYkrx+7UCKpPmaz84Undv+c1QzypPrY RpNtLZFUH6fbPaknuX/2+xJJ7p+9l0RSffzM7r88qT7urpqaQZ5UH3+z9YSeVB+PV03NMU+qj4d0 vCiRVB+X6vhSIrH1pTTYKSHVR9n7U/q7elJ9nKPJfiyR2H5amuxQiaT6KLUsT05I3q9+ZEKqj01t jZQn1cfy9vnwpPoYp+NGiaT6WEuDQxJSfZS1phdIJLb+uiY7UiLJ6y2XlUiqj3KvMVMdid0/Z2sK Pcn1x8ZIJNXHXzXZKwmpPpawPUCeVB+l1noficQ+v2iy/SWS6uPpqqlv4Yndj2xrHDypPjbXYI+E 2P4eGuyWkOpjoAa9E1J9fKTJHkuI7U+oY5E6kupjSQ1OS0j1saeO+etI7PycBmcmpPoo747nqiOp Pi7RZDNKJPb9R9XUCPak+nhHkz2XkOpjVU22p0RSfdyo41OJpProbfsZPLH7kW1NkGfbH6jtD9Sx P/sPCak+XtFk/5OQ6mNtDX6bEHv/ocHRCak+vpam/rwn9n1h1fQA9qT6WMTWwHhi++HoeE4iqT7O sn7Zntj9phoclpDqY2mrue6J7RddNV/wxPYr0GSTSCTVx206Rksk1ccsGlyVkLye/+CEVB+ltsVT CcnrpTaXSPL+yoMksl0v1a6X6ni/voBEUn3MatdXT6qPGTW4NiHVx4s2n+9J9TGRBvckxO4Xs2d8 T6qPPnb/5Un1cVH5N3UkuX9UV4mk+ljA6ml7kutLlXcenlQfZe3tfHUk1cdgDbZJSPWxhSbbTyKp Pua05xVPcj364xNSfbxXNftLPak+jtVkK0ok1cd0mux8iaT62MPuST2pPn5t+7E9qT5uqpr6J55U H2UtcqmH60n1sbsGPRNSfZynyX4ikVQf5dq6sERSfVxQNT0rPbHrx2x9pSfVx9FWn8+T6qOsbfiZ RFJ9jNLxhURSfZS5/CnrSKqPsVYPxhNbH0aTrS2Rbb3Ptt7n+OPD5hc8qT5WtvoFnuT+HvNLJNXH ETbn4knuN7+FRFJ9TG/PcJ7Yz4sm6y6RVB9jrF6QJ3Y+W5OdK5FUHz1tTaEn1cdITdZZIqk+yrni MYmk+phKk10skdj9lZrsVIkk92v8SCKx/V412ccJ234Fbb+C4uN1OyY8secPTTatRJL7rV0ikVQf h1dNvWRPqo+jdMxRR5Kfb0+XSHJ9mEklEjsfZWssPcnvk38pkVQfT2iyDxJi369rcH1Cqo81NNlA iaT6eMbeh3lSfUypyX4vkVQfd+l4SyKpPvbRZD0kkupjSMlfR1J9zK3JTpJIcr2LiepI7HylfUY8 qT5KbfHJJbLt99r2ey0+hmqyNSWS3C/pQ4mk+lhPg+EJqT421GC/hFQfO+hYoY6k+hihySaWSKqP eTS4OCHVRzdNdpREUn1cUzX9CD3J9x8fSSTVR+mVPWUdSfXRSYORCak+Su+9hyWS6uPPOl6VSKqP kzXZghJJ9bGKBsckpProocGRCbH1tXXMXEdSfZxi9xueVB/9NNkGEontF63J1pNIbH8P29/hSfWx qSbbViKx/V41OCsh9v5UxzR1JLbfq44udSTVx0ANeick7zd9XCKpPv5k8/meVB9vaLKXElJ97Khj uToSW49ekz2dENvPQoPdE1J9lLnrExKS+0W/JZHY9+uabGxCqo8XzIEn1ccSmuw3Eomt76DjJYnE 9mvUYOeEVB8P2PykJ3Z/ZdX0R/Kk+ljO6p94Yver63hbIqk+Su+9VSWS6qPUPplBIrH75zTYOiHV x7k6Jq4jqT5OrJp+L55UH3+196We5Ho5x0sk1cdqVlPKk+qjXFvPkEiqj59rcFhC8v7bThJJ9fG4 jqckEts/SpN9lZC8vnBjiaT62NeeZz2pPkSDezNCfSypyYZLJNVH2fvzUUKqj0002Dsh1ceCGpyT kOrjEx1/kEhyf7E5JLKt/9HW/xi/f06TDZNIqo97NdnnCak+3rI1MJ5UH1NosgslkurjbR33SCTV R7m2niKRVB+DNdlaEol9H6RBv4RUH/fZ+2NPcj3pURKJfZ6z+w1Pqo/fWD1LT6qPo3UsXUdSfVyl yWaUSGy9C022lERSfcxk/Tw8qT4uszkXT6qPZW3Pvid5P3IniaT62FaDXRKS69O9JJFUH7tr0DMh 1cc2GgxOiH2/ruMziaT6WEiD3yek+ijfZ5+E5P4efSWS6uMpHa9IJNXH5TomqyOpPkqtoFslkuqj 7A1bpY7EPr9oss0lkurjfTuHelJ97KnJfiaRVB/lWfb1hNj9Lzo+lkhyvZynJZLqo/TuXFQiqT6W 1mRHSyS5X9KZEkn1MU7HLRJJ9bGW7S/1xO6/tfo4nlQfgzTolZDqo6smu1oiqT6O1zFLHUn1Mb/d b3i2++fa/XPFx0hN9nVCqo+JbM2YJ/Z+TJMNksi2X3TbL7r4OEyTLS+R2PrammwSicTWt7Sf35Pq Yz7rl+1Jro/7kkRSfTxm9ec9yfWDNpNIqo87dbwpkVQfR2myxSSS6qO/jmXqSKqPXXUsXkdSfbxj 92SeVB9faLIHE1J9fGTzT55UH8tosgMkkurjTasf7Uner36JRFJ99LX7c0/y+/XyDtmT/D5oYonE zmdrsl9IJNXHh5rsyYRtf6C2P9D4fjg6vpJI7PO+Bn0TYvu/2JpCT6qP3TTZ2hJJ9dFdkw2VSKqP d8s7ZYkk94+apo6k+vi1BkMTUn2sZD0bPKk+OmkwMiHVR6kdvYZEkvtZHCSRVB+n2hpcT6qP53Q8 KpFUH6dpsvkkknx/eodEUn1sr8k2kkhy/aCzE1J9zGPrCT2x9fk12fMJqT4+1nGTRFJ9vGdzdJ7k /S9XSiTVx0M6XpZIqo/FNPhdQmw9aatf4Emeb1hHIsn1Pv9HItv79fZ+vfgoawlXlEiqj0XseuJJ 9VF6h18tkVQfAzTYPiG2vrYm+7VEUn1MrcnOk0iqj9Pt/bEn1cekmuxyiST3azxZIqk+hliNYE+q j3U0+G3Cth9O2w+nYz5qU4ls69O19emKj3PsmuJJfn96ZkKqj+N0/KiOpPootZP2lkiqj3U1ODAh 1UcZK9SRVB9barKtJJLq43Ydb0kk1ccFmmxWicTer5drTB1J9VF6m+wukdj6dJrsGImk+viJBhcm pPoovRknriOpPvbRZKtKJLl/w8EJqT421WCvhOR6wUtKJNVHb6tJ50n1MViDbRJSfZS9UB8mpPoo vffukUiqj1I76TKJpPpYTYMjElJ9rKfBAQmpPspcS5c6kurjFlsD40n1cVDJW0dSfZS1c7NLJNXH 47ZnzpPqY2d7h+yJ7bemwZUJsetxNRiVkOpjcU12tkSS+/HtkxA736DJzpdIqo/Si/A2iaT6OFfH dHUk1cdATbaBRFJ99LA9hJ5UH8fY58OT6uO+qtl/7En1sa2tn/Mk7/c4KCF2f7aOJetIqo+nNNln Cak+9rbzhSfVx7NV0xPIk+pjtPVH8sSeP3S8IpHk9R8DE1J9HFI1NWE8qT4usvkWT6qPW3V8JJFt Pem2nnTxUda+TCeRVB9/02SPJqT6KO86XktI9TFF3fQQ96T6WF2TDZfI9v60vT/tY3NPZX2UJ9XH sprscImk+nhMx2sSSe6nNXsdSfXxiCb7W0Kqj7I37Md1JNVHqXXauY4kz9/OWEeS5/cHSyTVR6mF 21Ui2/2m7X7T4uN4W+/hSfVxlI5Z60iqj3FVU8PRk+pjB6sf7Umun9xNItt6sG092OLjLk1WSyS5 Pm5niaT6uMFq0HtSfayvwfCEVB97Ws0xT6qP3TXomZDqo78GfRNSfZTvs2dCqo8Hdbwkke3npf28 tP2Soo8yt3BJQqqPJ3U8I5FUH3012a8kkurjEx03SyTVR+kd/phEYvt5arIjJJLq42hNtphEUn2c UDX9PDypPg7VZEtJJNVHZfVgPKk+Trb1+55UHwtYjQtPqo89dCxYR2LXw9gctifVxwua7K2EVB8P 2/pKT6qPRTXZIRJJ9fFXHfdLJNXHBzpGSiTVR+nteqlEkut/vJew3V/Z7q8sPkSTXSkJoT7K2ttu dSTVx706XpZIbD02q5/kSfVRauM8KJFUH+frmKiOxPaP0jFbHUnuT3hBQmx/U5uv9aT6eM2uKZ5U Hz+3/XKe2HpKmmwSiaT6KHOTNyak+ii1Tk9LSPWxgu0h9MTWQ6ma/vKeVB8za3B1QvLz7acJye9P 301I9TFEk60hkdj1/LbG0pNcD3b2OpJ8fbkmIdVHmXu6QyKpPi4s+epIqo+NrZ+YJ9XHShocl5Dq 40tNdn9Cqo/3rSa/J9XHWZpsLomk+thSg90TUn3cYzWDPKk+7rCEnlQfpZbDbhJJ9bGZrVn3pPro osEtCak++mmyDSWS6mNNe+fhSfUxiwZXJaT6mFuDSxNSfQzSsXgdSfWxX/l6HYmtb6lB/4TY/g0a nJyQ6mN5TbaXRLbrP9r1H8XHSB1/lUhy/eRrJJLqYxPrAexJ9fGyrTn1JO9/eUUisfvndNwkkVQf YzXZXxJSfaxlPYE8qT4+tv2lnlQfp1g9fk/s/peqWZPsSfXxrCZ7OyG2Pr+O0RKJrQerya6VSKqP 53S8KZFUH6VXw0iJpPpYRZOdJJHY/si2x9QTux/Z7sE8qT7K2uwp60iqjzI3OXkdSfVxQNXs2ffE 9n+x+VpPqo+FNdnBEkn1sbqtn/Ns14+168eKj1GabFKJpPpYzHpWelJ9DNRg24RUH3NocGVCqo+J NdkfJJLq44mqqefgSfUxmSbrXkdSfWyuyfpLJLl+0J8SUn2sZ8+0nuT+6htLJLY/oSZbTyKpPna0 9x2e5P3Z9yWk+ijvjkckpPoYpsk2kEiqj8812eMJqT7m1eCyhOT+t5cmpPoYocmmkkjy/dhGEkn1 UWoFLVZHYut/aLJtJJI8/3JbQmz/Fw3uyVhx9yMvUkdSfZS1HrcmpPqYy+6/PKk+5tNkx0hk+7zf Pu931HPcNyHVx0NVs3/Qk7w/6vGEVB87abBDQqqPnW2+xZPq4wYdn0okub7DuxKJff9hayw9sfUt q2Y/lCf2+VaTrS2RVB83VU3NZE+qj0s02QwSSfXxatX0l/ek+vjI5mA823oXbb2L4qOy/die5PPH gxKJfd6384Un1Uc36//rSfXxvI7HJJLqY30Nhiek+ji0avqHe1J9lNqvXetIcn+x2yWSvF5qYomk +rhIx1cSSfVRamuNlEiqjz/q+FAiqT56arKtJBJbX1uTHSiRVB+D7f2xJ9XHRLZ+zhN7PtVkU0gk ef/+FQmx9bY02TQSiT2fVs16dU+qj2ttTZAn+Xq7hkRi6+VocGZCcv/bOSWS6qPUXltaIrH1Pm1+ wZPq469VU3PMk+rjQOuh5Un1cULV1ITxJM83TF1HUn2UXsgL1ZFUH9le0y3B5483q6bHvCfVx4q2 JtmT6mML+4x4Un2U2klnJKT62FpHjzqS6uOc8m/qSOznRZP9RiLJ74POSIjtN6/JjpNIqo8ZNLg+ IdXHw1XTY82T6qOXjpXrSKqP6ewdsif2eU6TvZiQXJ/u4oTk+cpPJJLq4xNbA+JJ9TGj9fPwxPav tHdinlQfM1nPOU9yfctfSCTVx1WarKtEUn2U3llvSyTVx2E6Zq4jsfWUdCxdR1J9zGzXE0+qjz/r eF4i2/6Vbf/K4mNbDXZJSPXxF032YUKqj+Vs/tqT6mMWTXaqRFJ9nKnJ5pFI7PpCHXPWkeT5/VXr SHJ/wm0kkurjabvGelJ9rKPBQQnb60t7fSk+TilfqyOpPq7XZFNKJLa/mPUn8KT6KL2zfi+RVB8v 2PyTJ9XHjTpGSyR5f/YidSTVR6kldZlEYvc3aHB8QvL19hSJpPoYo+NliSTvR74yIbZen45J60iq jwt1TFZHUn28psn+JyH2/akGuyWk+jhXk80lkdj9yOW/oY6k+hhWNXuiPKk+jtIxXR3Z9rNo+1l0 7N+/WyLJ/RtulEhyP75S49OT6uMJTfZZQnL/hgMTkvsB75eQ6qP0AppIIqk+dtegZ0Kqj1012C4h 1ceT9r7Uk+rjUevB50k+n36ekOrjxKrpB+RJ9VFqi58tkdj365psZomk+pjP6uF6Un0spckOl0iq j0812RMJsfNROp6RSKqPzzXZownb+cp2vnL884sm+yAh1cdIW0/oSfWxnQY7JyTvJzxDIqk+drH6 J55UH6tbjQtPqo9X7PrqSfVRap0uJJHk/ep7SyS2n4Um+6lEtvMN7XxD8bGuJttNIqk+TtUxbR1J Xg8zQiKpPn5h6xs8yfNRnyYk19t6USKpPk6y+w1Pcr2LpyWS6qOTBrcnbOez2/ns8fXGrZ6DJ9XH IE22tkRSfbyq4wGJpPq4VZNNIpFUH/016JuQ6uMuS+hJ9fF+maOTSPL69X0Sks+nk0ok1ceXZQ1/ QqqPY6umx5on1cfj9jzrSfVxmfUU86T6eFfH7RJJ9fGI1Rf3pPo4smp6Anliz6e2fs6T3A/4QIkk 98OZtY6k+rjUes55Un0cbseDJ7ZfkgY7JKT6WNL6qXu2+7Pb/dnFxxDr2eBJ7m96hkRSfayiwTEJ yZ+XngmpPkqvuTcSUn38VpMtK5HY/rcabJ+Q6mM2WyPlSfXR2dYDebb119v668XHB5rsqYRUH+eV f1NHUn08WzX9xDyx9eg12dES2b5Pbt8nFx+7adArIfZ5X4NrE2LrGWiyrxNSfQysmvrinu18djuf 3dG/cm6JpProo8k2kUjs+lN7XvGk+thDx4J1JNVH6VU5u0RSfdyjyb5MSPXxnCZ7OyHVxxIanJGw Xc/frucvPvbTZKtIZFs/qK0fVHyU3iZ3JaT6mFmDaxKS+53sn7D10fpo648l9bWthpIn1UcJRiVs 1zu06x2Kj6k0uDkhuZ7S8xJJ9fFy1dTY8qT6eEHHwxKJ7RddNf1/Pak+TtPRpY7E9ovWZL+WSOx6 Bx2L1pHYegb2/seT6mOM1TDwpPrY2erxe2LPpxoMSkj1cbUmm1oiqT4+02QPJWz3e7T7Pdr3H8nn RccNEkn1Mb8mO0Iiyf3F3k+I3d9g6z08sev5bb2HJ9VHubYuV0dSfZTPxkiJpPooc/lT1JHY/h6a 7BCJpPrYUYP+Cak+FtNkF0gk1ccUmmyURFJ9rGTnC0+qj2d0PCGR5P0ezyak+phcgzsSUn2UtUBv SSTVx4c23+JJ9XGo1ejzJPePui0h1cePrZ6DJ9XHQhqck5Dq4wodU9eRVB9vaLI3E1J97GL9kD2p Pt7UZK8kpPq4RcdYiaT6qDXZNRJJrr8+u0Ri5/c1uDIh+f3pYRJJ9VHeDS4jkdj3hTYn50n1sYEG +yUk10OZVSKpPpbR4JSEVB97abJfSiR2Pa6OietI7P4oTdZTIqk+elnNQk9sfVwNLkxI9VH2Hn8s keT9yC9LJLm+9qMSSfXxhe3v8KT6uEqTdZVIbH1+ex/mSfUxTpPdn5Dqo4s903pSfZS9LktLJNXH 6zoekkiqjw3tfZgn1cd8muwEiaT6KLVgPklI3g+0Uh1J9fG0JnsvIfZ6WzX9oT2pPi6w+QVP7Ppk TfZFQuz7ZKsZ5ImtB6vJ+kok1Uep5dBNIqk+NrL6855UHwdajWBPcj3p4QmpPj7SMUIiqT6OsTVj nuTnl/cTUn1Mpskuk0js+0Jbr+6JrW9ZNT08Pdt60m096Y5+J1cnpPp4TMdTEkk+n76YELufUJP9 SCLb9drteu3i46canJewfb5tn2+Lj9Lr9kmJxNbXtjk5T6qPUjv6fInE9pvXoHdCqo9+OpavI6k+ FtbgrIRUH5/q+KNEUn1couNLiaT6OFyTLSGR2PuPqumZ7Un1sYYGhyak+vjS1md7Un300WBAQqqP 28u5UyKpPs4t/6aOpProa/WjPak+yt6wFyWS6mO0vQPypPq40+YYPKk+brAa457t81z7PDd+PUyZ s5RIqo/rNNmUEondL6bJtpdIqo97q6Z+gWf7/NI+vxQfc2hweUKqj+U12d4SSfUx1tYEeZLr474j kVQfz1n9Rk+qj6NtvboneT/huIRUH5tosj4S2fZvaPs3FB+lduNdCak+fm01HD2x9Rx1rFxHUn3M pcmOk0iqj91tTZAn1cc0muxsiaT6WF2TDZJIqo/TrIaSJ9XHWhocnJDqY1VNNlQiqT4W0WS/lUhy fcsHElJ9fKDjVonE7hez+jie2PV0mmxTiWz337b7b8fX/9AxXR1J9XGQJltWIqk+Si+PLSWS6qPs dekskVQfI3X8VSKpPrprst0lklwP5QGJpProrcGuCdv7j/b+o/iYW5MdK5FUH4va+w5Pqo91NDgo IdXHVhoMTtjuv2333xYfG1s9XE/y+fRAiaT6mEKDEQl/iD46fl2r3+SaOsbf9H1XsN9PrmMbHcvZ f8dy9u+X+/t3kvG5vu1nKf9uOvv9lDpWbPJVs9p/Y/n+m+pfWsbioXUTr2R/r7v9f9PTPot76NjM /bdTXZV4629xVerS9IK6ut+5uv8bXN1rrh4Euyr9vCZ0VeLM1ZLSuCrvN6muznGuzvkGV2eZq/PA rrrU/+yqxJmrznXjasqa62poHa+Dmash9T+ug/+Kq47fywR/Z8oJvk7/+/+tY2km+/2Ex4S4a3v5 //RHE/zZDPb7OXVsYmtLC/tZnbW97L1X1f2NHps+8XqPju8xkd2vTvjra/u1yfifbZHxP1/nsn7Z 2B4LP5xj4f7veSzcZsfC48mxcP//4lhYoj0WfrDHQrkX+z7HwgLSHAtl/Zs/Fjq+x/c5FpZqj4Uf 7LFwzvc8Fk6yY+HS5Fg4539xLCzTHgs/2GOhS/39joVyM1iOhenreCx0fI/vcyws1x4LP9hjYej3 PBZ2smNheHIsDP2ex8Li/+K94/8Pz2jlXXKPCZ7R1rZ3bf4ZbU0dW+ooP/Nq0OdZ76q7xd7VKmUN f926KjVfJnRV4sxVqU1XfuZXhetqf+dq/29wta+5OgDsag7nao5vcDWbuZoL7OrW6p9d3VrlrkbY uf32iuuqp3PV8xtcdVwHt6nad5X/6t/vlnzd/9uNlANtXn603quV/z8PmqgZxzb/h8tk5Rpc7Vb1 q3qPr5H8r/3q1LXcI752VHfZXEfhqZ1urS5X3rv4YrLWZPNVO09y3D4HzzT52jOtuXB1rH7t9tV+ 3LX8d479YJ5qJR336t89Z94RVSf9/dbrdup66qfzjP/OG2w7X7WPfm25evCQ8vvy61iNV3nn8WGF za/j9uliLjpylvwj9M9XmPfDYY9sfXld/uVMO3Ubf3QWPqJ/dvOPPxzW3EPP3Xfm6moZrV9bT792 0Exz9+1wP/3fV851raYbPU/V440x4/+8fL38+eZlDcDQ8Yd49f/Ks8Eydt/1Xc8GZQ3EMvr3li/3 /+7ZoON7/Lvvlf/V47jj13/jOJ5rz+5y4h7dpbAcR2/uEY7jdfxxfP2YeapxenxMvGdzHN87+p+P 43K8rtVr8PjfT6o/1XIfzlNtMKY5jgv9cdyRs+TfZ0xzHJ/aOx7Hx46Jx/HVY779OH58TDyOt/g3 juP2HPt/7xx7+97dZdxe3aWwHBsD9g7H5rrfdI49f+/8HFuOiXJe2F8TdNXjtoxRG9w97BEd2Tm2 I+eE59il+rTnWH+OLc9r3+cc+4Q059iOmnQTnmPL9/h352t+iOfYbvt1lzP37S6F5TgavW84jn/x TefYKfbLz7HFazlu5h6/YlWPGf37X680Q9fytewc25FzwnPsuB3acyz9HLvUoO5y8cDuUliOjXED w7H5y286x8406D9zju3IOeE59tR+7TnWn2P3/57n2CF2jj08OcfuL//+POgP8Rw7xZDustbg7lJY jqMzB4fjeL1vOseOHvyfOcd25JzwHNtrQHuOpZ9jLx+qz1c6CsuxMWRoODbX/6Zz7LFD/zPn2I6c E55jx+3SnmP9OXaO73mOndbOsT9NzrFzyL+/vuCHeI49s193Gbuj3sv2a47jPv3CcbzBN51jh/f7 z5xjO3JOeI69a1B7jqWfY+ca0F1O3EnPswPsPdZO4djc8JvOsRMP+M+cYztyTniO7TWkPcf6c2yZ V/o+59jrquYce18Vz7Hle/y763Z+iOfY23fRZzEdheU4OnSXcBxv9E3n2PN3+c+cYztyTniO7Tas PcfSz7ETb9tdturdXQrLsXF173BsbvxN59gHe/9nzrEdOSc8x961Z3uO9efYnt/zHLuRnWN3TM6x Pat2Pdx3rQOYcM/SkXWM167+eb2cj7O9vmvaOPo79vr+b88R77nr14j6v3D96qPXLx2F469ffcI5 YhN/jhii14QR5frVpzlHHOquX1PY9at8hrtOcH0px1fXCa5fk3Zcv/r84xyxkl2/3tw3niM2SK5f A7/j+nVie/36QZzj+muw8Hec40rvxU/s35S+P4u5c1zH95jxW85xpfbFz6rt9fy4m/7vLtXgaiH9 GTfT3w/Q3++ovx+o32Po+E/O7vrVMus9VVmf/o+f6++/72KOyphmgrjLP37u8ZzUvtZlgq91xD/0 +9defbvLmTt0l8Ly+Zuib/j8bxruEfTzvpKObn3tHsF9/uf++5vsyasT7RrdrX+38V8/dnT8/Hfk HH+PMNo+/wck9wijk3uE0d9xj9B+/n8wn/8rv2Ndz7FlTV7pp6B/72Tl1XX8/Jfv0eVbPv+l5snP q0H62S6fjbmqX+pnvPf480Dz7zrbZ7yz3StNbPcKnSf4s07tsfBfPxbO/I5jofSMLLXgSy2cC5Rn JcdC+R5dv+VYGBCuBfHsP+ExMYk7Bjruj8vXJ5vgmOk0wd9rn2H/u8+wfTbqLk9v2F0Ky/VhoY3C 9elX/vr0uF4TZtOx1kbN9enNb3mGLdeP0RM8ww5Mrk8dOcfPU9r16dBD4/Xp6uT69Mh3XJ/G/n/y DFs+y+t/x1zMOfb5mUmKg6o62M3FdHyPqb7lM12ee7/tbm7qCZ5tO7nn3EmSr2Wf4wk/B1PZM2Vl P2f5/f8BMCgV73iLFwC= In most of the situations, the p-values (and thus the confidence intervals) are nearly identical. However, in many situations the Behrens p-value is noticeably more significant. Also note that the arrow is pointing to a few extreme observations (using the “.” instead of the “o” for points make these hard to see). I believe this is caused from the problems already seen with the R code for calculating quantiles from the Behrens distribution.mean( Welsh p.value<0.05 ) = 0.0560714285714286mean( Behrens p.value<0.05 ) = 0.04464285714285711-mean( Welsh ci ) = 0.05607142857142861-mean( Behrens ci ) = 0.0496428571428571From this information we see that the Behrens distribution had an observed significance level of 4.96% and Welsh had an observed significance level of 5.61%. While the Behrens method calculated confidence intervals more inline with the specified significance level of alpha=0.05, in terms of agreement between the number of p-values less then the significance level of 0.05 and the percentage of correctly specified confidence intervals, the Welsh approximation performed better. For Welsh, the p-values predicted 5.607% of the confidence intervals would fail, and 5.607% did fail(R output says that they are identical up to 15 significant digits). For the Behrens method, the p-values predicted that 4.446% would fail while during the simulation 4.964% confidence intervals failed. This relatively enormous discrepancy of over half a percent, while producing better confidence intervals in practice, shows the limitations of the Patil approximation as implemented in the provided R code because the p-values do not accurately depict the Bayesian belief in the confidence interval.More information can be gleaned from the following SAS table.Equal MeansThe FREQ ProcedureFrequency Percent Row Pct Col Pct Table of welsh_ci by bf_ciwelsh_cibf_ciTotal0 1 0 2674.7785.0396.04470.8414.970.883145.61  1 110.200.213.96527594.2099.7999.12528694.39  Total 2784.96532295.045600100.00Unequal MeansThis simulation was performed over these values. n.x=c(3,5,15,30,75) mu.x=c(0) sg.x=c(1) n.y=c(3,515,30,75) mu.y=1:8 sg.y=1:8“515” should have been “5,15”, but currently there is no time to rerun the simulation. Each combination of parameters received 2 simulation iterations for a total of 2560 iterations.H4sIAAAAAAACC+1bXWxURRQ+s/zt0kKKKVgCCaVAqApaEAqWRRiwpQVKC/2BVME2LaSFapa/FkkT +kAMajSLqYaHRqrBqIQIGh5IaJQXw488EK2Wakx4IEI02pY0kQfIes69M+ndubN3t7WNC/duc3Z+ 7r1z7nz7na9z584wAGhFG4M2g/I+gHNo8nO9GOAdtMz84gIABtVbAE6PMc+fiNYoTxwHcAkr9zGA qQyiPqWfjgN/3lhYB/ugBkJQDxy/Q8axeWipaH50LfPjLHm1Ht1DiNGdAPRFIhGrn7Dpl03AL46+ GtBbIwz3k218/5Axe8tUbHnaFOYP9WfBst9WNlOeIDpxcZ5xTiXWWSCDeecBHvRmweHC7qr30IJT fqkivPz3suCfHd1VaX1ZxnktFd1VA6IvU4Q9gTbdOBrdt07TAXsFr82be6+5PZRtYJexh+4zzUhD eOzinHvNqcaps7dMh3MsjHWbsI76IXGdaiDFjOvO43F+p79Z9pOOV6HVNRH0g78Ps+QnOfw+wz1f rc/WtOPEhb8ierxGhgv+NPr9jtVwFg5xRukJ/zdwG/NXFuUwK91bEc8w1l1aOyeN7vMAcqaTfu+9 nHXM7YRjmN+xwZ924r7Jgd1lAH+81dUMoq9Ups/WY5UBuPXwiGx3vDgufZL/YL/Jhc/32blQ2m/n AvHXiQtt/cnBhWQ5fwOmq9FyzDJkimtNtAY/XyPXvvLZy7HazRB5FdMZot3dWFgotEAemybys9DK 0TrQ5jLzmrPMvEeDh6vv8IqffueyjcloGxU2R8SnnngGOzEu9qMmZ6IiL4QmI04OYu1+Q49SRN9T Bu/fSMeLuhRLnSxbsR1qHI+upptxnF3HWWstZ5RSHPXVmjFVOGEevDbueMuPaRPX3mqcHxXHAxi3 QbTUOjOO/Uocz4a3RQ8mQpvQ1Ozd2UZ9WOg9wPEWGcfSJ/nvFJoearLH8Q2NpvfF0fR0L46TJo6/ 9DnHcTvaEjxwEs87ycyxlxrH1MakOHFcAa9jzO7FyKX4yIRiLNVg3X7Mp5j3DgFhMk+xMNbELuqY /zHjxXA16OgY00ZDg8K7OBuLRilpwLZdNg16SdWgLoz7mWgHdpkadLc3WoOIdcS7I+iANILscul3 zTfQQhoNkj7Jf7vQoIHDdg06p9GgG3E0aEAzrtz2HzTo/4phit0S5hzDR0UsPUXPPpgeZNExLNsI OMRwNeYLkFtmDO/EyK2FNzA/UfQ3oLGhxOpo4Zcn8nSfr6ItR/OJFCwpeWIxIkK2R9elD/YFVoj+ yd+C2q/Ak3JFuclnloPiPOof/Z7b0cqw/hDaVuXesy2+3IQVlXc4YFWDabVLsbqmYHUtBlZXBFbX XYzVUhaNFZV1WD3PTKyWMfdi1aFg1REDq48EVp+4GKsUXzRWVNZhFfCZWE3yuRerJp/9/6AOqwO+ wf+DTlgl4zN6TgNnp+o5o5TGp/frbePjfHV8fB6fex/guDO9wRwfX1Ge0VvFGJjm5DL+DreEsB0a e1F7NF8mx8cpAgvpk/y3iLm29Dft4+OwZq7tXJy5ti7vGd0VcwCkBYfizAFUi7QBz2vA9LAyByDb GOPw/FBu9O1ZtEgkIJ7rAx4XkooL1xLkwreCC10aLlwbAhcWe1xIWi7QuDkRLjzNTC6sYnYuyDYS 4cISjwtJy4WOBLnwgeDCaQ0XOobAhVyPC0nLhRRfYlyggTtxYarPzgXZRiJcWO5xIWm50JQgF/YI LrRquNCUIBcWDXPs+Dg8TxfRc6vleZrKNB+qPk+vE/dCfV7r0rkHFavVoqxi9SLaKp+H1VUWjRWV dVhdZiZW3zP3YrVZwWpzDKxKBFZlLsaqB6Kx6gE9Vt1Cr34F92JVo2BVEwMrqe21w8DKm39L3rUW jeWc3SrjjFKay11SbptLLrCt9+rNgiBaablY7+Ww1oLW86ZZ1lqEe+1zydKnsd6r15xLrm7XrPfq 1az36o2z3usxWWuRK8YSTuNdsvloK/G8F2jNhDLelW0wh/FuqdE3c6yb7GsVU7dy1lrJGaXEna5K G3fXxXoP0lepfw8yS6xrN9csIk/w/EhwWhrV6d6DSJ/W9yAzT3rvQdyuq6fWc5aBRilxo3G9jZuF sXT12PqR0VXp06qrFz72dFXV1ass/jwC6WonM3W1m9l1ldqIN4+wFHsntTWgmUdIyvXgxaixGzmj 1FgPvtHG46JYGptaPDIaK31aNbb1lKexbtfYMyWcZaJRStw4UGLj5vpYGhsuGRmNlT6tGjvzM09j VY3dHEdj64TGrhIaW6vRWGpjbNy52hzjT10PnOw6e2ENZ5c2c0Ypcal1jY3LG2LpbPuakdFZ6dOq s3e/8HTW7To7s4CzcD5nlBp7O/Nt3NwYS2ehYGR0Vvq06uzRM57OqjrbA4np7GUwdfZPsOtsDySi s0sfSZ2tK+LsZiFnlBKXFhTZuFwcS2cLi0ZGZ6VPq86WnvV01u06GwpydnsFZ5QSN5YHbdzcFEtn y4Mjo7PSp1VnFwQKfZ7ORutsTYI6WyJ0dr9GZ2sS0NnFCYxnh4tPkbB3EYtKn72cLHu1tlveUbVp ylzZy6WWt4N+b9fLaB+O0jv4RwFbwm66srdLLVuxbNOUp2vWN7yP9qTYC+ZWbAm7hRasIpoyd8Ba Xq/bZ/cMvcNh7sWWsHtO2WenlrkD1vJ6FduHAvNlLsaWsFtswWq3pswdsJbX6/Y85mB9o4uxJeyW KXse1TJ3wFper2Jbj/VLxR5Jt2JL2C23YPWzpswdsJbX6/af5mL9TRdjS9jlKftP1TJ3wFper2Lb JTCn/apuxZawC1qw4poyd8BaXq/bC5wncHUrtoTTSmUvsFrmDljL61Vsae3uCrF2fG2Ce4cni3sF 0Tbl/wUjwfPSYFIAAF== The difference in means between the two samples is detected a significant amount of the time.H4sIAAAAAAACC+1bbUyVVRw/5wJ6EXHogOl0E1EmNTN84UUE5agpvhWFmCNUTN18IXcFBDJmfHDJ IBs2an5gSYnmW4TNGgqVH8wYs2EbZWu1VWvp1oqXseUHG/3/z3NOPPc85z73QrCuPs9l/3tenvPy nN/9/X+c5zznUEJIFVgI2HSMuwhpAROfWxsJqQWLe2rjakIoKXqOkAshevkJYEWiYBgh1yGzmBIS Q4nXJ+dMGHGnh5I1pJjsIB6yhzD49mjXEsAmgrmhaxEPM8TlfOieeCjeCSG9g4ODxn7q9H7pePhi 0Nde6K2IjPSTqH3vnDJrewy0fC2SrvL0xZPUHzPLMY4QnWxL0MpshjwDZCThCiEPeuLJ4ew7+W+A ZUz+Ph/xcvfHk7+23cmP6o3XylXm3ckf4GOZzG0K2DTtqvfY2vUOaAHUTZ/TX97gSdSwm7of7zNK Cz1wrW12f/lEreis7dNIC62DvKchD8chcI3RkKJavStwnd3tKxfjxOv5YLvKEPqh34ca4pEWv89I y8v5iYp2rLjwx6Aar9HhgjsKf7/KTxjt/ZhRDE+6PyOrIOxYkESzxyeQl8JOVP4SPSHlp6K5pA7y rq+cHYX3WQqcaQeMC6Fs45x2Ug3xbevdUSfv6xzIeTGBPIC8NFdJKcbxEwV1lv3eXY6h/jlROY5j IfrE/jP6dC6cKzZzIafPzAXkrxUX6vuCgwvBUn49hFlgSXqaxPG6OlpDn4+Aa5dd5rSvdqfyuIzp dN7uPkg8wbVAXIvl8Zlgm8Au4e9N9TrXqH6Pmvxl3WV53/zGRBvY3gaJzYP8g/6wguwGPS6G7wOk BEbogVplmq8cgrwSMgnKRAyN4994BMcE4+N42pgn0kach+vTY6vvuk/PuMrollZGMUSf6mg1+XSq 7NMD4K8ZYL+26j7tlnwafTe7sESLj4NRVYBfoQ5jfl2v2adFn9h/O9f3yjKzT99W6HuvH32Pdnw6 aHy62WXt0w1gi+HCKSh3iurzMNmnsY1IC5/eA/E88OXd5CB4MPpHHNkIqR2af+s+iT98ODcRR18I 1bHzuuZ+xHgxUg06GqLbWGhQexuj968xiiFqwIY2kwalyRrUDX4/A6yxTdegez3eGoSsQ969Ch2g RqB5uAZ5FBok+sT+G7gGkVfMGtSi0KDbfjRoQDHH3PIfNOj/8mH03WeotQ8f5b70GD4HQXiIevuw aCPcwocLIb5a+598UPsvfIDsJC/z560wg3+Gj9BXxwq/dB7H+9wOlgbm4iExhNgT9eERoj2sFz00 FrKUj0/8Fth+HhRK4ekyl57O4OVwfPh7bgXLhfwKsOele0809GUnrDC9zQKrHRAW2hSrTgmrTh9Y dXCsbtkYq2TqjRWmVVgtojpWqdS+WDVKWDX6wOodjtV7NsYqwuWNFaZVWIW7dKwiXfbFqsxl/j+o wqrUNfR/0AqrYHxG777IaDYYhtr89KJpfrxEnh9fgedeXFdrvajPjzukZ/QqPgfG9bmpf9ZVeqAd nHthezmGdbcIjoXoE/uv5Otuca+Z58d1inW3Fj/rbt3OM7ot1gBQCyr8rAEU8nAvlNsL4WFpDUC0 EWLx/LBJG9t8HF9VOH+uD3e4EFRc6AyQC59zLnQruNA5DC4sdLgQtFzAeXMgXHic6lxYTs1cEG0E woXFnAMOF4KPC40BcuEtzoULCi40DoMLKQ4XgpYLEa7AuIATd+RCjMvMBdFGIFxIc7gQtFwoC5AL +zkXqhRcKAuQCwv0ueOwufAoPE+vxedWw/M0pnOJ+Xl6DdizYDjmlTZde5CxyuJpGatlYMtdDlY3 qTdWmFZhdYPqWHVQ+2K1TsJqnQ+ssjlWG2yMVRfxxqqLqLH6iuvV18S+WOVKWOX6wEpoe94IsHLW 34J3r0VpM6P3PmAUQ20PZbNpLTndtN+rJ55kgG1p5vu9LPZa4N5etC9zvii/DVbXY15LFn1q+716 9LXkogbFfq8exX6vHj/7vR6RvRYpfC5hNd9FmwuWCeWW4J4Jab4r2qAW890cPrbwh2CvYvRlRqtb GMUQufNDi4m7S329B7nfon4PMpPvcZ9FarQ73gXlBzNiozBP9R5E9Gl8D5J4ynkPYnddjWtitP40 oxgiN+6dNnEzw5euhjaNjq6KPo26euNdR1dlXb1J/a8joK5epbqudlOzrmIb/tYRkmF0SaS/3LhP Ldg1tuksow/OMIoh8qjorInHmb40tvrs6Gis6NOosa83ORprd41NPM9owzlGMURu9J4zcXOZL42d eH50NFb0adTYxPcdjZU1dp0fjd3FNTaNa2yBQmOxjVC/a7VJ2p+8HzjYdTa7Gvh4jFEMkUsDx0xc Xu5LZ+dVj47Oij6NOjtw3tFZ289laxktqIG5bC2fy9aYuJnlcy5bO0pz2RqzztZdcnRW1tkuEpjO fkp0nf2ZmHW2iwSis8kPpc7OO8Lo4uOMYohcqj5u4jLzpbNRR0ZHZ0WfRp0t+NDRWbvr7K0qRt1g GCI3KqpM3FzhS2frq0ZHZ0WfRp11T1nrcnTWW2dzA9RZxnV2t0JncwPQ2YUBzGdHis9abscBi80u czpYzmptNbyjqlekmXSWS05vJeqzXS+AvT1G7+AfBmwRu1jpbJecNmJZr0jHKvY3vIn98rNgdsUW sZtjwGpQkWYWWIv6qnN28fgOh9oXW8RuvnTOTk4zC6xFfRnbv3F+yM/l2RVbxG6BAat9ijSzwFrU V515fBLyi2yMLWKXLJ15lNPMAmtRX8Z2D+Qv4mck7YotYpdqwOpbRZpZYC3qq86fIubf2RhbxC5d On8qp5kF1qK+jC2+R0vj51Xtii1il2HAiinSzAJrUV91Fjid42pXbBGnTOkssJxmFliL+jK2uHd3 Kd87vjLAs8OT+L0S3jbG/wEyvwuabFIAAF== The Behrens distribution of p-values looks indistinguishable from the histogram for the Welsh approximation.H4sIAAAAAAACC+1bbWwURRh+Z/vBlQI5DCUlkFAKDRWhvQOKLRy1d5xwUE8bbYGcFIsWU6SSoy1t xSb2R02IVnMkJjSxQhM/wg9jqpb4g8aQGCM/TGwihsRoYiIVEiN3bRr1R2N9390Zujf7cW1t48Hd Ju/Nx87Ou/PsM8/OzM4xAOhGy0BbjdarAAyiiePbIMCbaAWPB/cCMJiswjxFK78YrVkUzAK4hpkt DCCPQdxR82EWOHZmwj5ogWMQhibw4m9YPVeEtgTNgbch4lm6uJz/NIZhRncCEJuamtL7iWh+2SL8 8aKvE+itGeZ6FKu/gbx1F/Kw5pOLWGV4rBAe/Xl3B8UJor6rRWqZg5ingwyKhgAmo4VwNnAz9Daa Z/mPIcLLMV4Ifx29GXLGCtVyXXU3QxO8Lcu5PYS2Sj0b37ZhzQE7gtfu3DDe0R8uVrHLP0n36VTD MJ67un68Y4ladN2FVTDIIpj3JOZROwSueSpSTL1uCM97b491iHbS+RBaYztBP/18mC6+1Ob5zLW8 nF9sUo8dF/6YMsdrfrjgcNLzW3PYzyKH/IzCPseXcAvj190uFlhUBC9nne/amLP4kTvfbYMI5l3b s95J99mGnBmm543XDGwYhnMYP1rtcPb9rXGg5vkimMS8cqW1jeJ0OPGayt9vdFCoHee7sjkWwif5 94xpXLjcYuRCzZiRC8RfOy68M5YcXEiW8tUYotyBS0tDAb9WQ2v6+Ay59qliTFvVm8/jMqareb0v YWIL1wJxbiWPr0WrpThmjvBrMhTtHlX5q7rtrfvhN6+og+75CYnNU/zoxbgPjqMet+DvKWjF0mG8 ql3tK2cwrwBTBXAIY814tslwvhWWYR250+28F8/lmFE8m6f1eSKezcPlurzcaaxsr8+VnuNsNWNh 3x+aZgyH/MyFRiH12Z6QQTM2y5oxgXrgQRsIaZrhkDSDtCHQ0KrGs7FVndhvSecpPxIzaobwSf6H +fvjp3ajZoyYvD9iCd4fK9KakTSa8Ylirxn9aNvxxCUsd4lp4zxZM6iOpTaa0YTxOtSK43AaFYD6 RwEEMXVM1Q+tT9KDz+Em4tQXMjXs4s45HjBezFWDejI0WwgNOlLvZyNH/IxC0oAN9QYN2iJr0A3s 92vQquo1DboTjdcgYh3x7jV0QBpBFuYaFDbRIOGT/PdzDWp41ahBgyYaNJJAgyZMxrCH/4MG/V99 mPruU8y+D/fwvvQwzbMwPMPi+7CoI8emDzdgfK/6zj+tvsVPwQvwCp/PZen6Z84c++pC4beTx+k+ n0MrR1N4CLqQPDGLHiHqo+tWTLcFdvH2iWdB9ddhoR083a5oaQ8vR+2j51mP9gzmd6Idku69WOcr lbCi9FEbrI5h2JCiWI1KWI1aYPUrx+p2CmNF4xE9VpQ2w6qJaVg1s9TFKiZhFbPA6i7HajyFsRJa rtd2M6zalGltt8MqGeed/QE/c6JRSGOuxoBhzFcij/mGcC5Ha1HdAW3Md12ad3bzcR2taeXfjXSF sR4aT1B9Nbq1qlyOhfBJ/rv4WlXt68YxX8RkrWowwVrVjfS8MyXmtaQFnQnmtdRXgmgnsBx9VTgr zWtFHVk2Y2KaL2zB1pWA+14bc/icVYyB07xIHl6MzpAX33Ne/GnCi9FZ8cIFZWle3BfrYIl40Ujv CqbxopMZeSHqyLThRa3aNmKFK82HJOZDbIZ8+IXz4R8TPsRmxYeyNB+SmA/tysz48KKi8aFHMfJB 1DETPrjnqA8PwjxrP81ndPMsSl8E4zxrH/82QW3ek6JzUhmrKp6WsapEe0xJY3WFxWNFaTOsPmca Vl+w1MVqk4TVJgusijlWm1MYK9InPVZmelWp06sBmD1W6bWG5P1W6qn2s84DfkYhrVvdOWBYNys1 7NeIFoIHLbOa79ew+VZKe//Ivqn5umMELRI1rpsJn+p+jai2btbbZ7JfI2qyXyOaYL/GA/KtdAd/ P9qN48g2ou3GchX0zVMax4k6mM04rkZtGzOM25Jxzfda0M+2o1FI3DkXNHDXZbXm+0HQfM13Ld8D uw7eUO+4EctPeVY6Kc9szVf41K/5Bt5Nr/mmuq4O7fCxYjQKVW5gKHHTbaWrfVh2PnRV+NTr6q33 0roq6+qVBHtQGriuXmaarn7FjLpKdWQkmB+XqatnLG6fSbJrbLjCx26V+xiFxKPyCgOPt1ppbG2F b140VvjUa+zHA2mNTXWN7fb42MQuH6OQuBHwGLi5zUpjGz3zo7HCp15jA++nNVbW2E0s8RokaWw+ 11iPicZSHYnWIN2qxroM+/mSXWd7S1FnS3yMQuJSbamBy9utdDZcOj86K3zqdXbFR2mdTXWddW71 sSa3j1Go6pzbwM0yK52dcM+Pzgqfep0dvJzWWVlnL8LMdJb+C0U6OwhGnb0IM9HZsoQ6O1d89nN7 C7E4qBjTybKvtR7i92rKaa+071VO14P5PthnQdvbuRDfO+4HbAm7Nha/t1NOexVrrMX1Zvtm6f/a 4ymMLWHnkvaCymmvYo21uN5sn20J/06cqtjK2E0mSLdbpM325dI30N4E2OrHDsv4vQKvm+L/AmyK ZQP8QAAA The distribution of the differences between p-values, while skewed, looks much more centered then the distribution of the differences in p-values under equal means.H4sIAAAAAAACC+2dCbxeVXW3z15hCAmECGEIYoAQJAMSSEK4mW5yqymlDgVHPkVIwDAGiAESkEBA BhkUo4LSMoXJohWhiNbKFCsoAkXKYOVzwoEGS9EEKYSKH9/a9z2vXvY64SYk0ZT/k99v8dz3zb13 5X1YZ+99ztln71RV1ekefTxe73GhVdVNHu0/97+9qi7w2HH62/+yqlJ11tP9qv0Pb31/P4/Z7W/c sKqW+JtzU1VtlaqX/dnvug2rvhM3qPap5lYzqznVEVWX/3dO99/t4rGpR1//Z7S/3rDH1+X773TO SflfUlXLXnrppZ55FrXypo39P12e60jPNrt6tX+GV3/VuWs6sd9Om2zlv/mIKdPT4mG3df/N45Om /+ET5vdyLPE46K19Bz7+0tDu92/Za3D3z/zsM5tVWecmVevfnH/nJftOTwcsG1rtf1i/gfnr/N64 K6enaz1m7NuKqhpaDe/YeGD++tzJre//3rl9Bx7onDjsmflfGjii2922Rw/3/w7s5hz/u1t3fmb+ pt3/gp02GVzdlBb5e+/w9/LnaHvdqttU6v65W/zvu5Yun9/+nPnv3+/xoXlZ/R///6QeX2/2Cv9/ Xu33r+r7b3VO89ij9brasc7V+jRVtW8dn3Dp77X4emW/d9fs0sOKKmh/T37/bdmLx688nkiR7X/H TtWyHr/h9KnNXzf/6flvGt4j9/rs4xJPNiJFqvr4tCd7V4pU9fEGf/HPDVT18X2P36ZIVR97+ovL Gqjq46D8b7BIVR+XerJhKVLVx394PJUiVX38hSf7WIpU9fEeT3Z4ilT18QVPNiZFqvoY7smuSpHK 7cfxKVLVx8892dIGqvoY6cnOS5GqPu7z2NgiVX2c6/FGi+T8hfOX7ONtnuzoFKk8Pj0mRar6+IbH sylS1cdtnux1KVLVx2EekyxS1cdFHrtbpKqPH3v8MkWq+rjek41Kkao+LvQYapGqPp7yuDtFqvqY 79Fhkao+dvBkF6VIzuc4n2v76LRIfOADH9HHIR5TLVLVxxGe7KgUqepjiSezFKnq482e7JQUqerj OI+9LJLxGOOx7OOzecxukao+rvMYbJGqPr5VX08vqerjIY8fpUhVH5/yGGKRqj5O9hhnkao+/tKT XZAiVX0cXp/PllT1cbbHrhap6uMUj7EWqVwfu1mkqo9HPFakSFUfD3j8JEWq+tijnr9fUtXHtR4b WaTy9Y/JFqnq49h6PlBJVR8LPSZYpKqPOzy6LFLVx888vp8iVX2c6DHGIlV9fMJjuEUqt6ejLVLV x91V65mokqo+FuefsUhVH+M92cIUqerjZo/fp0hVH3ntk+dSpKqPg+vxaEnl+adfTJGqPvL6Wg+l SNn1tjz6WaSqjwc9HkuRytfHuixS+X72nhZJfVAf7edvX0iRqj6u9Ohvkao+Pu+xmUWq+jjUY4pF 0p7SnlIfDc97eEy0SFUfZ1at9XFKqvo4ur5fW5L2lPY0+5hdtxclletjqkVyvHC88HwUzyNzvNCe rqmPvS1S1cdJ9XyPksrrGUywSOXz/QkWqXw+N9Yi6W/pb7OPI6vW+gUlVX38sq6HkhwvHC+cz0Uf M+vxeUlVHzPq89mSnM9xPkd7SntKfdB+UB9rz8es+npYSeXrHx0WqTw+nWSRtB+0H/hoPl46LZLz Oc7nGK/jozcfu6dW+1mS9pT2lP4WH5zvUx/4WHs+Hvb4WYpU9bGPv/h4A1V93JR/3iJl13P0F1c1 UPn66VSLVPXxPk92aIpUXs9xvEWq+jit3iO6pKqPBR4jLVJ5/Y9fpkhVHx+q+5OSyuvRT7ZI2f2R q9b+SCVVfZzlyfZJkcrroQywSFUf+/uL0xuovF7fFItU9XFMPT4vqerjlqq1Pk5J5f2SuixS1ccz 9f3akqwPw/ow2cf8+vgoqepjbn3NtKTy+dyuFqn8PHKXRXI/m/vZ7fFph0Uq7/c63CKVxx8dFqnq 4zNVa3/Gksr78X0+RTIfhvkwrC/VPF4fa5GqPo6v77eUpP2g/cBH9DHSk12RIpXH69tYpPL9l06L VD5/6bJI2lPa0/Z6WxMskutjXB/LPo6q77eUVG5POy1S1cdH6vuTJXn+ludv6W+pD/pbjpc1XT+o yyJVfQyv1y8oyf197u/TflAf9Ler5+PDdT2UpP2g/cAHPjifW8372fXzxyVVfSyuWvtDl1T1MdaT XZ0iVX308xffbaDy80BTLVLVxyer1n5iJVV9HObJ5qRIVR+/9XgwRar6+Fzdv5ZU9fEzj39Nkexf yf6V2cdxVev59JKqPu716GORyvubdlqkqo/l9fWOksr9y9MpUnZ8WvcnJVV9fMxjO4tU9XFu1Xqe sqTy/Ze9LVL5+f0ui1T1cUJ9Pb2k8vPqUyxS1ccij1EWyf7q7K+efcyrWs+nl+T+Lfdvs48n6s9f kvsv3H9pn891WiTtB+1H9nF6/flLKs+3nGiRyuOx8RbJ/FPmn9KeRh8n1p+/JPOTmZ/M+JT2ozcf M+rrgyWpD+qD+drUBz5Yb5z64H4l57f4YPxBe4oPfOADH/jAB+MP6oP6wEc5/6PLIpX3z+6ySFUf p9afv6Sqjys9trJIVR8355+3SFUfb6/XhCmp6mOQJ7smRcrO//AXH2yg7H4WnmxGilT18bDHYylS drzuyd6fIpWfF3uTRar6ONuTdaZIVR8XeOxgkao+fuVxd4pU9fE3nuyTKVLVxxfza4tUvj422iJZ 35L1Lbm+zv7ZvfnI+7vuZZGqPkZ4sstTpKqPr+Z8Fqnq44Oe7AMpUrY99WTvTpHK/e0eFqn8vNg0 i1T1sdTjeylS1Udeu+DTDVQ+v93QIlV93OPxZIrkfI7zuezj5Dxmt0hVH1t4sutTJPPHmD+WfSyo WuvRlVT18e8ev0iRqj7+zmOYRSq3H5MtUtXHB+p72CWV1+u7P0VyvHC8MF5nPNabjws93mCRqj6u 8Rhgkao+3lLPRy6p6uMqj20sUvn62BMpUtXHf3uyf2ugcn87ySKV1z+dapGqPj7hsbNFKtfHRItU 9fHlen5lSfazYD+L7vlj/uLgBsqu9+nJDkiRnO9zvt9eL7jDIpXP97e0SOX9tMZZpPJ+FsMsUnb9 0/oaUElVH5/J32uRqj4u8ni9Rar6OLO+nl5S1ces+ny2pPJ+fKMsUtXHj6vWfOSSqj4+VbefJVV9 fLwef5VU9XF+/flLKt+fG2CRytc/Oi2S+TDMh2mvXzjRIlV9fNRjqEVyvHC8cD0ZH735OLi+n19S 2cc0i1T1cWg9/6Uk/Qv9C+P15vaj0yJVfcz0mGKRtB+0H+31pSZaJONTxqf4wEdvPl6sP39J6oP6 wAc+8IEPfOADH5zfUh/4wAftB/WBD3zgAx/0L/Qv1Ac+8IEPfOADH/jABz7wsb762Ca1Pn9J6oP6 wAc+8IGPNfHxpaq1X2VJ5fmFd6ZIVR/3e/w6Rar62NGTXZkiZdfr82QHpUhVH12e7LQUqeqjrye7 KUWq+njJ459SpPLzYhMskvEp49Ps49j685dU9XFS1VpPu6TyesFTLFLVR95rbrxFqvo4rmqtX1CS /ebZb57+Fh+9+Ti6bi9KqvqYXbWe1y/J/ELmF7b7206LVL6e/K0Uqepjuce/pEjaD9oPxh/4wMfq +Tiq/vwlVX0cWX/+khwvHC/4wAc+Vs9Has83LUl9UB/19aAui6Q+qI/s47MeQyxSef/KaRbJ8cLx gg984AMf+GD+2LqcHzTRIjleOF7wgQ984AMf+FiX84O6LJL6oD7wgQ98rP5+jV0WSX1QH/jAR28+ bvP4TYpU9XGPx9IUqerjao8tLFL2+VtPtl+KpD2lPc0+9vdkJ6ZIVR+HVa3nf0qq+pjiyc5Mkao+ ZlWt59NL0p7SnuIDH735mFt//pKqPo6v5xOWVJ7/Mc0ildczmGqRtKe0p9nH6R7DLFLVxxyPvSxS +XjptEie3+f5fdpT6qM3Hzwv9nIfM+p6KEn7QfuBD3zgg/U/1vT8ZaJFMv+U+aeMP2hPe/OxQb3e R0nqg/rABz7wwXp91Ac+8IEPfHB9nfrABz7wgQ984AMf+MAHPvCBD3zgAx/4wMef08fB9ecvqbw+ /1CLVPXxrMdDKVLVxxfya4uUfb7Sk+2TIlV9/F1+zyJVfXzdY1mKVPVxuSfbKUWq+rjLk/2+gcrj 03EWqerjfzy+liJVfazwZA80UNVHXktqeopU9TG+PmcpqerjYU+2rIGqPg7wZAenSFUf+3qy2SlS efwxwSJVfZxdX/8pqerjNI9dLVLVxzmerCNFqvr4iccDKVLVx2fq46Okqo/RnuzsFCn7PHI95iip PP6YbJGy18c8nkiRqj7O9Rhskao+tvNkl6RIVR/3erIVDVT18V5PNjNFqvrI1477pUhVH339xZIG qvqY6THJIpX3w3k6Rar6OMNjZ4tU9bG5J7s6Rcrej/J4k0Wq+rjFk22aIlV9vMGTXZwiZdej92Rv S5Gsj8v6uO35yVMsUnl/oA6LVPXxLk/2oRSp6mOiJ/tIilT1cZ8ne76Bqj5Oqe8/lVT1cUQ9v7Kk 8v7ZEy1S1cdZOa9FMv5g/MHxEn3cXl8fLKm83+veFqnqYxNP9vcpkueReR6Z6x/N69FPtkhVH/M9 Rlmkso+RFql8/3ayRar6+EHVeualpPJ+r+MsUvn+7VUpkvEH44+2j6kWSX1QH9nHqfX145Kcz3E+ 1+5vOyxS1ccJHqMtUtXHWE92Zoqk/aD9wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCBD3zgAx/4 wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCBD3zgAx/4wAc+8IEPfOADH/jABz6OqVp7ZpdU9THK k30iRar6uNHjxRSp6uMQj06LVPVxtyf7fw1U9fHpus0oqerjd1VrD5ySqj5O9hhhkYzHGI+119fu skhVHws9hlmk8npKu1uk8n5J0yxS1cffV603Sqr6OM5jrEUqr88/2SIZfzD+wAc+8LH64/VOi1T1 cbbHEItU9fFFT7ZVilT1cUH+XoukPaU9xQc+8IGPNb0/N80iqQ/qI/s4px6PlqQ+qA984AMf+MDH 2t1vfoJFKu9v2mWRHC8cL/jABz7wgY+1e39uqkVSH9QHPvCBD3zgAx/4wAc+8IEPfOADH/jABz40 fUyzSFUfn/foY5GqPk7zeKNFqvp4zuMbKVLVxyKPrS1Seb7DVItUfv5lO4tk/MH4Ax/4wAf9y5r4 2M2TnZcimf/B/I/sY7bHXhZJe0p7ig984AMfa+Lj1Pp6WElVH7/y+HaK5HjheMEHPvCBD3zgg/Vx /zQ+ZtafvyTHC8cLPvCBD3zgAx/4wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCBD3zgAx/4wMf/ 1vnaYyxS1cfrPNm1KVLVx+0eT6VIVR//7vFoilT1sbRqPc9QUtVHftbl2gaq+vhbj34Wqerjyvwz Fsl6W6y3xfNz0ccdnqxPilT18VOP+1Kkso8HUqSqj7d5siNTpPL6hS+lSFUfx3qyv06Rqj4WeIy0 SOXx2FSLVPXxEY8RFqnqY09PdkaKlO1v/cVHG6jq4/3+4sQGKq+3NdYiVX086cl+1EBVH0/V1ztK qvpYXF8PK6nq49L88xapPF7fwSJVffzC454UqerjCY/vpEhVHzd4vJAilc9vJ1mkqo8cnRap6uNo j3EWqVwfHRap6uPvPDaxSFUfeWz+rQaq+tjIX/xLA5XvN7w1Rar6+IrHb1Okqo9D6vFXSVUfR1Wt 9fhLqvo4zGNvi1T1cafHr1Kkqo/PeGxukao++tfz1Uuq+jgu37O0SFUfz3jcmiJ5HojngbKPefX8 l5KqPg73GG+R3H/h/kt3fXiy/VOkqo8vePw+RSrv/3JXilT18awn+7cGKo8/Oi2S8RjjsexjVn2/ paSqj1NyXotU9THHY7RFqvp4zuOfUqSqj094bGmRqj6OqefflqS/pb/FBz5685H3z5pikcrzgyZb pKqPCzwGW6Sqj0Ge7PIUqdx+dFok/Qv9Cz7wgQ984AMf+MAHPvCBD3zgAx/4wAc+8IEPfOADH/jA Bz7wgQ984AMf+MAHPvCBD3zgAx/4wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCBj7i+5a4Wqepj gic7NUUq78fXzyJl9xfzZFumSFUfN3o8nyJVfVzsMcAiVX3M9WT7pEjGH4w/8NHsY5pF4gMfrKcU fdznyZ5voKqP+R6jLFLVx0er1nrJJelv6W/xgQ98rJ6PGR5TLZL6oD7a+5tOsUjOXzh/4XjBBz7w QXu6dvvbTovk+gfXP7KPI6vW/p0laU9pT/GBD3zgAx+MT6kPfOADH/jABz7wgQ984AMf+MAHPvCB D3zgAx/4wAc+8IEPfOADH681H4d6TLJIVR/XePSxSFUf7/Zkh6ZIVR/f9Xg8RSq3p1MtUtXH1zyW p0j6W/pbfOADH/hYEx9HVa3nGUpSH9RH9nGTx3MpkvqgPvCBD3zgAx/4wAc+8IEPfOADH/h4Lfng eWTqAx/4wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCBD3zgAx/4wAc+8IEPfODjteJjA39xdwNV ffx91XqjpKqPv/EXpzdQ1cePPNmTDVT18XuPm1Okqo/765ooqepjX39xdgNVffyzx9MpUtXHAo9d LVLVx9WebEiKVPWx0GOoRar6+KXHPSlS+XxuskWq+viix+9SpKqPEzx2s0jWY2M9tuzjHI/BFqnq 43Me/S1S1cfTHktSpKqP5z2+liJVfezhyT6aIlV9zKr715KqPvKLbzdQ1cfmnuyqFKnq40iPvSxS 1ccZHq+3SFUfJ3sMt0jZ8xdP9n9SpKqP8zzZmBSp6uMGT7ZFilT1ke/Vbm+Rqj5+4fHdFKm8v8c0 i1T1cZLHCItU9XFtfc5SUtVHjr0tUrn96LBI5f09lqVIVR9z8/sWqerjbk/2YgO5H8X9qOzj8Kq1 X0NJ6oP6aN/f/58UqerjaI+xFqnq41aPp1Kkqo8B9Ry6kqo+5nmMtEhVH4d4TLRIno/i+aj280C/ T5GqPg6rx6MlVX1c7/FiilT1canHxhbJ80A8D5R9nO/J9kyRnN9yfpt9zKxa+8uXZL8C9ivIPo7N +S1Sef7YSItU9fFDT/arBjI/mfnJ2YfV61uU5Hyf83184AMf+MDH2vNxTc5nkao+8lzky1MkxwvH Cz7wgQ984AMf+MAHPvCBD3zgAx/4wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCBD3zgAx/4wAc+ 8IEPfOADH/jABz7wgQ984AMf+MAHPvCBD9bbeiUf+dPeliJVfYzzZKelSFUfF3lsbpHK+1cOtUhV Hzd6PJ8iVX2c6C8+2EDGH4w/8IGP3nzk/dUmWqTyfkl7WyT74bAfTvaR93Zd0UDl/V9GWST9C/0L PvCBj9XfD3iCRVIf1Ef28YIn+9cGqvr4iifbNEVyvHC84AMf+MDHmvi4umrt6VGS+qA+so+5HqMt kvqgPvCBD3zgAx/4WFc+Ts3vWyT1QX3gAx/4wAc+8LGufBxStfZTL0l9UB/4wAc+8IEPfOADH/jA Bz7wgQ984AMf+MAHPqpqqkWq+rjJ47kUyfpBrB+UfTzh8e0UqerjYI9Oi6R/oX/BBz7wgQ/GH2vP x3UeL6VIxh+MP2g/8IEPfOADH+vKxwX5ey1S1cdhHh0WyfHC8YIPfOADH/jABz7wgQ984AMf+MAH PvCBD3zgAx/4wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCBj959XOfJdkmRsvOTPdk5KVLVx7/n fBap6mNXT3Z5ilT18UFPdlCKVPUxwl9c00BVH3082ZdTpKqPYf7iCw1Ubj9OT5GqPp70uDtFqvq4 wWM7i1T1cYwnOyNFqvo4t+5jS6r6+JgnG58iVX2c4sn2T5GqPt7oL65voKqPSz1GWaSqj8ur1n6E JVV9bOIv7mqgqo+zPHa3SFUfm/qL7zRQ1cfWnuyyFKnq4zhP9o4UqepjN092XopU9ZFjikWq+rjH 43UWqerjk/UYvaRy+7E4Rar6uNXjhRSpfH+/0yJVfeztyc5Pkao+vpR/xiJVfRztsZdFqvqYV7XW oyup6uPM+vy+pKqPn3k8lCJVfWzvL77SQOX1Pt9okao+crIbU6Sqj8c8HkmRyuOPDotkfjLzk/HR 7GMPi1T1cWQ+x7VIVR//7LE8Rar6+J7Hj1Mk7Sntafbxw/rzl1T18XGPcRap6uMQj8kWqepjuccE i1SujykWqerjIk82OkWq+viUxxssUtVHroWzUyT7ibOfeNvHFItkP0/288w+vunxZIpUro8Oi6Q9 pT3NPt5az9EuqerjJE+2T4pU9XGLJ+ufImXro2o9P1hS1cdHq9Yz6iVVfbyQ51ymSK4ncz05+7jQ YzeLVJ4vleuhpKqPQZ7sjhSp6iM/e/y7FMn5C+cv2cexHmMsUtXHw3kOWYqUXU+pfr60pKqP26rW 8z8lGZ8yPm3P5x9mkcr1Mdkiuf7B9Q/GY9HH/Pp8tiT9C/0L9ysb1pOu66Gkqo9L6vkvJZk/xvyx 7OPwqvX8cUn6F/qX7OMyj40sUtXH3Kr1/E9Jxh+MP9o+9rJI2lPa0+71pD32tEjl9dg6LJLjheOF 60H0txwvHC9r6mOSRar6OLTuX0tyP4r7Ue3rp+Mtkv6F/iX7mFl//pLK5y8TLJL2lPaU9qP5/stU i+R8jvM51pOm/eD8lvYDH7Sn1Aft6Z/r+tgUi6T9oP1gPIYPfHD/ZU18XOyxhUWq+visJ+tKkcr7 z+1lkao+8t7hs1Okqo9rPNmeKVLVx7mebHqKVPXxHU+2YYpU9XGfJ9soRar6+JjHUItU9TGnnt9Q UtXHTzyWpkjZ/jZ/ZotUbj/GWaSqj4/U10tLKrcfy1Kkqo/veryYIpXnf0yySOX1tqZZpPJ6KNMs UtXHyfX8uZKqPs7xZO9Mkao+rsq5LFLVx/s82cIUqerjxPp+bUnuz3F/jvn8zIfheFk9H0fUn7+k bPvhyealSFUfx1Wt539KKp/vT7NIVR8H1+Ovksr9y3iLpL+lv8VH8/WxLotUXh+3yyKV15eaZpHK 1z+mWSTtKe1p9vGN+vOXVPUxo/78JTleOF7wgY9V8cHzldQH19epD3zgY237OKXuT0qq+phd10NJ 5fn8XRap6uOCun8tSXtKe8p4nfrAB/uLrYmPWfXnL8n8deavt58HyvVQUtXHCVVrv5eSqj4e8FiR IpX3F5tokao+tvdkX0+Rqj5urlpvlJTd39STjU6Rqj6u8NjMIlV9zPMXBzaQ+y/cf2H+afTx43p8 XlJ5vN5lkao+vl+11nMoqfz87TYWqerje55sRQOV13Pc1iJVfXy4au2XXVLVx+F1f1JS1cep9ecv yXid8Tr3o5rv74+ySOX7c1MtUvl59U6LpP2g/cg+jq4/f0nl+uiwSPZ/Yf8X5ks1r+/QZZHK92+n WaSqj0957G6RysfLRItkPMZ4rO1jikUqr3/aZZEcLxwvzC+kPlbl+scUi6Q+qA984AMf+MAH18eo jz/d/uoTLJLjheMFH8z/oD1dPR8/rz9/SdbnZ31+2tPm8ccUi6Q9pT2lv6U+8IGPNd3fo8siVX3s n1qfv6Sqj8VV6/mfkqo++vmLuxqo6mOpJ1vaQFUfz3iyJxqo6mMXf3FdA2X3K/Bkc1Okqo8Bnuy6 FKnqI0eev19S1cfVHttbpKqPX3g8miJVfSzx+O8UKbvehSf7TQNVfbzOWjVRUtXHck/2aANVfezr yY5Lkao+/tGTbZkiub7O9fXs4yv5ZyxS1UdK9f24ksL10cciVX2805PNSpGqPoZ4sotSpPL+QCMs UtXHY57sPxuoPP6YZJGqPvLY/NAUqerj8x6DLFLVx+c8Blukqo9PeLI9UqTyen27WqTy9dMui1T1 8V2PZ1Okqo/T6usdJVV9nFffwy6p6uN+j5+nSFUfB3iyD6VIVR8L6vPZksr3s/tZpKqP5zxuT5Gq Ph73ZE81kPnazNfuPp/z2NkiVX38Q37PIlV9XJ7n1Fmkqo+hnmxRilT18Zn6elhJVR+3Vq052iVV ffxlfU29JM8j8zwyPqKPr3q8mCJVffygvv5TUvn66RstUnn90wdSpOx+wB5bW6Ty+GNuiqS/pb9t r4fSZZGqPp6sWvNNS6r6mO0x1iJVfZxZ358sqepjUX29o6Sqj/M9drBIVR/frFr7Q5dU7m8nWaSq jzPyNWWLVPWxhSe7MkWq+pjjsZdFys7XrlrrF5RUro8JFqnq43iPcRapPL9wqEWq+jjSY4xFMh+G +TDZx8z6ekdJnlfnefX2/KCXUiTXk7mezPHSfP3juRSpXB8TLZL+lv6W8Rg+8LF6PuZ7vMkiqQ/q Ax/N6/NPs0jqg/rAB+e3nN9yvOADH/igf2F8yvGCD3zgAx/4wAc+8IEPfOADH/jABz7wgQ984AMf +MAHPvCBD3zgAx/4wEeTj5M9Rlmkqo8TPdm7UqTyep+/SJGqPs72GG6RsvuJe2xkkao+Tq9az7uU VPVxgid7R4pU9ZH3inpPimQ8xniM+afN/e1Ii1T1cZhHp0Wq+hjkyW5Ikao+jqnroaSqjyuq1nrr JVV97OQvbmgg4w/GH/jAR28+ZtSfvyTjdcbr2ce8qrW+Z0nl8dhki1ReL3iyRdK/0L/gAx/4WM3r 63X7WVJ5/fVpFqnq4xSP0Rap6uPLOZ9Fcv7C+Qv9Cz5WpX/pskjqg/po70/YaZHKProsUtXHsXX/ WpL2g/YDH/jABz7wsXb3n+uySMZjjMc4XvCBD3zgAx/0t3+6+5XTLJLjheMFH/jozceGqfX5S1If 1Ac+8IGP1fNxc9XaL7ukqo9vezydIlV9HOEvjmqg8vz1iRap6mOpx8MpUtXHBZ5s7xSp6uNqjy0s UtXHC57s4QYyHmM8xn6e1EdvPmbV9VCS+evMX88+/sXj+RSp6mNuPT4vqbweyhYWqerjw1Vrfb6S 9Lf0t9nHi/XnL6nqY9P6fktJjheOl+71k+vPX1J5/sdki1Reb3yMRar6OKSuh5K0p7Sn+MAHPlbP x6H15y9JfVAf2cf8+vOX5Pop1085XvCBD3zgAx/4wAc+8IEPfOADH68VH6l9v7Yk9UF94AMf+MDH GvjYuO5PSlIf1Ac+8IEPfOADH/jABz7+/D4u9tjeImWf3/d4g0Wq+niwaq1/UlLVx795smcaqOoj P3t8YQNVfWxjrTWUSqr6+LTHlhap6uM0j10tUtXH2fXnL6l8f+7G1EBRH/t4suNSpKqPPNa4PUWq +pjgyRakSOXn1b+SIlV9nOXJOlKk7P6VnuyvU6Ts+pa5DbFIVR8PefzfFKnqY7InW5gildcLfj5F qvr4jcedKVJ5v7XdLVLVx6Ue/SxS1cc0T3ZCilS+H9Vpkao+/imf46ZIVR93ejyVIlV9nOOxs0XK 7ofjL77VQOX9gf4hRar6uM2TbZAiVX308WQ3pEhVH49XrfU+SjI/iPlB2cepHiMskvX5WZ8/+zjG k709Rar62MFf/EMDldc/HWuRqj7u8mS/byDtKe1p9nGKx3CLVPUxs2qth1uS9pT2tL2e9AiLVPVx rsdgi1T18SWP/5ciVX0M8xefbyDrn7L+aff8oJzfIlV9fMxjO4tk/MH4I/u4weN3KVLVx5ae7IoU qerjEY8fpEhVH5t5smtSJPcbuN/A9aDm8dieFqnq4xaP/06Rqj6WetydImXvV3qyzhSp6qPLkx2f IlV9PODx4xTJ+IPxB9eDqA984GNN9xMfY5GqPg6uz99K0r/Qv9B+4AMf+MAHPvCBD3zgAx/4wAc+ 8IEPfOADH/jABz7wgQ984AMf+MAHPvCBD3zgAx/4wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCB D3zgAx/4wMeq+3jUky1roPL+yI+lSFUfd1St/QhLKq93Mc0iVX181ZP1T5GqPvJehINSJP0t/W32 cVj9+UtSH9QH/Uv0sacnOytFqvo4pK6Hkqo+5nnsZpGqPvb1F2c1kP6F/gUf+MAHPtbER96r8poG qvr4rMfmFqnq4wiPDouk/aD9wEfz/rddFsn1D65/4IP1tVelv51gkao+DveYZJH0t/S3+MAHPvCB D+5HrSsfEzzZghTJ8cLxgg984AMfa+JjRt2/lmT8wfiD4wUf+MAHPvCBD3zgAx/4wAc+8IEPfOCD +VLq86Xw8XIf53tsb5HUB/XBfP7o42sez6ZIVR+DPdnfpkhVH7t4sk+mSMZjjMfwgY/efMz12NMi lec7TLVIVR+3efw6RSrXR5dFqvqY7bGXRdK/0L/gAx/4wAf97drzcZzHGItU9XGoxxSLpP2g/cAH PvCBD3zgY12OPzotkvqgPvCBD3zgAx/4wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCBD3zgAx/4 wAc+/jf6yHszbmuRqj7GerIzUqSqjwc92TMNVPXxgCd7voGqPv7L45spUtXHSR5DLVLVx7X5tUWq +ljoySalSMZjjMdYXyr6+ErVWj+ppKqPD3iyA1Okqo/rPV5Kkao+HvH4fopU9XG3J3uxgao+kr/4 dhMZfzD+8HjS464UqerjbI8dLFLVx689vpMiVX0c5sn2T5GqPjbxF3c0UNXHdH9xbgNVfXzQk70/ RTL+YPyRfcz3GGmRqj6+7LEiRar6eDRHilT1sb0nuzhFqvoY6MkWp0hVH2fmvBap6uOttYOSyuv1 TbZIVR8nerzJIhmfMj7NPv7Wo79FKu+vPtEiVX0M92Tnp0hVH7mt+HgDVX18y+OJFEn/Qv+SfZxe zxcrqepjgccbLVLVR752vI1Fyt5v8GSfT5GqPjo82SkpUtXHUZ7sHSlS1cftnmyDFKnqY6bHJItk fVzWx2V8yvn+qrQfky2S54F4HuhD9bHx6Qaq+shzTX+ZImk/aD+yj3n1fI+Sqj4+kq8pWyTPR/F8 VPf8U4+9LVLVx70eP02Rqj4+7DHaIlV9fN3jNymS81vOb/GBD3ysno+Dq9b+nSWpD+qj7WOqRXL+ wvkLxws+8IEPfOADH/jABz7wgQ984AMf+MAHPvCBD3zgAx/4wAc+8IEPfOADH/jABz7wgQ984AMf +MAHPvCBD3zgAx/4wAc+8IEPfOADH/jABz7wEfd/6bRIVR/XevSxSFUf3/D4dYpU9XGMx1iLVPVx sycbkCJVfdzhySxFqvqYk/NbpHJ7+nSKZDzGeAwfzevB7maRqj7O8djeIlV9XO6xsUWq+jjFY1eL ZP859p/LPn7ryR5qIP0t/S0+8IGP1R9/9LVI6oP6yD4e83goRbKfJ/t5crzgAx+sn7ym669Ps0iO F44X6iP62MBf3NVAjheOF3zgAx/4wAc+1pWPWVVrD+CS1Af1gQ984AMf+MAHPvCBD3zgAx/4wAc+ 8IEPfOADH/jABz7wgQ984IP5p39OH0d67G2Rqj7O9djOIlV9POXxzRSp6uMD/uKEBtK/0L/gAx/4 YDyGj7XnY6bHFIuk/aD9wAc+8IEPfOBjXfqYapGMTxmfcrzgAx/4wAc+8IEPfOADH/jABz7wgQ98 4AMf+MAHPvCBD3zgAx/4wAc+8IEPfOADH/jABz7wgQ984GN1feS5t59soKqPGz1+lyJVffzQkz3Z QFUfT3h8J0Wq+njaY0mKVPVxrSfbLkWq+ljucVuKVPVxtSfbPkWq+niPJzs0Rar6OCN/ZouU3V/d k+2YIlV9nOaxs0Wq+rjBY0WKVPUx25O9PUWq+hjpL65qoKqPPBb9XIpU9XG6x1CLVPVxmcfGFqnq 4+sev06RyuP1mSmS68lcT84+bvV4KkWq+viGx3+lSFUf7/VkM1Kkqo85HqMtUtVH/rS3p0hVH5/2 GGCRsusne7IDU6Sqj0vr8XlJVR+bebJrUqSqj5s9nk2Rqj7yuf31DVT1Md9jhEVyPsf5XPaR701e nCJVfXw1j1FTpKqPKz02sEhVH+d5bG2Rqj4WerJJKVLVx089/jVFsj4u6+NyvTD6SJ7sy6mBoj6+ 7/FwipTdb82TjU2RstcLPdmoFMl8beZrd1//8GSfTJGsR8969Fz/aL6+3tciVX28kK+BpEhVH/vW cyxLqvo4x2Mbi1T1cafHf6ZIVR/H1cdIScYfjD+yj7wX8m4WqVwfkyxS1ccCjx0sUrk+Jlukqo+8 dsFAi1T1scLjaymS6+tcX+d8Hx/4wAc+8LGufCzxWJoiOd/nfJ/jBR/4wAc+8IEPfOADH/jABz7w gQ984AMf+MAHPvCBD3zgAx/4wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCBD3zgAx/4wAc+8IEP fOADH/jAxyv5GObJLkyRyuvlPJ0iZfdX9xhrkcrr89+QGijq4ymPJSlS1cfBHp0WqepjiieblyIZ fzD+YH0Y6qM3H1/weDFFqvq4ut6TsKSqjzd7sg+nSFUfIzzZeSlS1cd2nuyzKZL+hf4FH/jozceZ VWu99ZKqPg6tWuvxl1T1cZjH3hZJ+0H70b0fsMfOFkl9UB/4wAc+8IGPtedjRr7nYJFcX+f6OscL PvCBD3zgAx/4wAc+8IEPfOADH1z/oD7wgQ984AMf+KC/xQfHCz7wgQ984AMf+MAHPl7bPo70GG+R qj5O8hhhkao+rvDYyCJVfZxc10NJVR/3efw4Rar6uDT/vEXS39Lf4oPrhb35YD2ll/s4vWo9P1hS 1cdcj9EWSftB+5F9zPKYYJH0t/S3+MAHPvCBD3wwHqM+8IEPfOADH/jABz7wgQ984AMf+MAHPvCB D3zgAx/4wAc+8IEPfOADH/jABz7wgQ984AMf+MAHPvCxej7af272X/KPFl+v7PdOrL/uV7WeD+yo /x0d9c93/OE3pe5cr/RZ8s8Nqr/ezGNSK1/1+vrfmH//e/ybxtev51vr9eT6+6bV/28+6PGu/Dy8 x/uKf7uqq/z6oFdwNdM5Q9TVvYWre1fi6p7a1f3CrvZKL3eVXze5GptarvZOuq4WF64Wr8TVFbWr q4VdbWovd5VfN7nqZy1XA0zX1XyL/WCTqxPtj/3gq3HV/jr1+J7Neryv/v3rqpa2rb/uWROp6NtP 8p/fosffbV1/vYPHu6vW3ouZR9braH2kHndW05Z2vefR/+hq/44+9Xi155+X6j/v7v5su3d/vk08 NqhJLaw/tXDvKtbCnXUtPNJQC/euRi2MoRbW21rIY7FVqYWRqVULU1OshfbvWJVaGEctrLe1sHgV a+Hiuha+2FALi1ejFsZTC+ttLeSx9KrUQrJWLWxtsRbav2NVaqGDWlhva2H+KtbC7LoWzmiohfmr WAt7vsqx42vhHG3f+lrv+B6vD6ziOdo+Hu/3yJ/5zaLns6WrafXr0lWnx1TD1ePp5a7y6yZXP0kt Vz9Puq4WFq4WrsTVqbWrM4RdDSlcDVmJq+1rVzsKu7q9ermr26tmV7fWbfudla6rAwtXB67EVbsf PKjiWuWr/f7hDe+XP/tO55x6XexlPlbL/z/P6tOKRa3/4Wnj3AdXc6sjq5nV7OrV/uk7MI8RD3jT 9HT/btNT5iV976h2dN6z5x7przbepTpmw08tmLNVv+rJ742tFvl7S96888D873z2N0OryTn8excP u63q618f9Na+Ay9ZMbT7N+93yC7VAn+vw44/IX+d/yzy151PPTI/s/XnUwv61y7aOXP+2/zvJw57 Zv6DSy62/JPbHj28uzozH/S/u3XnZ+a3xtA7bTK4uikt8/fe4e+d2G+nTdrut+o21ToSBy0bWnUt Xd799/n9/PcH5DkA87pLvPrfcm4wvh539XZukOdA5H0ZJuTxf3Fu0P4da3pd+dXWcfvPuqjjFaOn p3EembmOrh0d6jiVdXzL8qHVi14fS0a36vieZS+v41yvfzXj+O6vN/JP1fHM0Gq/5a06zizruJ0z 51+wvFXHl3wr1vGi5bGOb1r+ynX8yPJYx+9fgzqmjf3TtbEzxkxPj+w5PWXm2hg+JtSmrayNfcuY 5jZ2x+r+6vrclo7ceuB7q/SHoUBuY5ra2HbOnm3suG/TxpZtbD5fW5U29tHUamOfSrGNzb9jTe/X rI9t7OxdpqfHh01PmbmOxu0S6rjPytrY/XZpbmOz11w3O1Xnd/+LP+Tf/9LkrQfm95ra2HbOnm3s i/fQxqq3sbcMn56Ge2R218bwUJsbrKyNvWR4cxubayK3Cws9wUCv2xzf2e/u+Q96NLWx7Zw929hL 7qONLdvYhavYxp5Qt7HnN7SxC9Oa3wddH9vYJa/3Gho5PWXmOtp+VKjjDVfWxnaMWjttbDtnzzZ2 xgO0sfLj2CHT09ff4OPYIfU4dkiozY1WOo4dsnba2HbOnm3siw/SxpZt7JBVbGO3rNvYEQ1t7JC0 5vML1sc29t07TU+LdpyeMnMdVTuFOt54pW3sTmunjW3n7NnG3vUwbaz8OHbQ9LTHzj6OHVS3sYNC bfZd6Th20FpqYwfFNnbG92ljyzY231dalTb25qrVxt5TxTY2/441nbezPraxewyenq7d1mt5cKuO V2wb6niTlbWxgwavnTa2nbNnGzv8MdpY9TZ20aZek35+1U2vjQM2DbXZb2Vt7Ambrp02tp2zZxt7 1w9pY8s29sBVbGP3r9vYwxva2AMr5sP1Ng+g5zNLH7f4et/q5fPlytdNz/ruU8eFvTzru7ptxNNF /3WbrYP+a/PpafYA7782b7URPxoQ2oj+ZRtxgvcJt/mxt2JAq404t+i/Nq37r3wMD+zRv+T6Gtij /9qodtHOmfNPrvuvJ38a24j9GvqvOb30XxfRf60XbdxR/uJNvbRxP/B4vv6ZH6bWv7FnG9f+Hdu8 Qhu3wL/+i2pWdYQfH7OqY6vjq938M77Pv57tXx/hX8/x3zGv+8g50d/Nd70HePT/4+f6w9f9a0c5 Xtfjdf8/fu5ublS/17/He+3X6/v49YAtp6f7t5ieMrvnxWwZjv9NwxjBj/fJObasxwjF8b/TH65k 96suqvvo4UcN735/0bJ4/Ldzdo8RltXH/y8axgjLGsYIy3oZI3D8rzfH/5d7mddzWb7v6X9xpX/f lc6bLB7/+Xds9grH/xG5j/bjflb1YT++8/GxY/V2fzWzuy1oHZN963HPJj2+7lOPhzYr/q4vdbHO 6+KyXuriSx67p9a6ONc5r2ioi/w7Br5CXcwO/ULsCfr3+P++YVED7bFyfn/jHjXTt8f3cT67bs9n d7vpLemsG9+SMnNf8ax/XfRVm5V91SPeP2yfz1P9Z3Jf9eQrnM/mvmRZj/PZOQ19VTtnzn9Z3Vdd 9J+xr7qpoa96sJe+6tnXyPlsPpb/ppf7Movr42fblB1U1TnFfZn27xjQS1v/SiO7zXuc5/Ytznk3 bHiv6TjueRwMqM8vq/pz5q//P8CmQiaE7QoA The artifacts noted in the Equal Means section appear to be more prevalent in the Unequal Means section. There remains a strong linear correlation between Welsh and Behrens p-values.[1] "mean( Welsh p.value<0.05 ) 0.72316776658562"[1] "mean( Behrens p.value<0.05 ) 0.685654741229594"[1] "1-mean( Welsh ci ) 0.0545328238971865"[1] "1-mean( Behrens ci ) 0.0493226814866273"As seen before, the Behrens distribution has an observed significance level closer to the 5% level then the Welsh approximation.Unequal MeansThe FREQ ProcedureFrequency Percent Row Pct Col Pct Table of welsh_ci by bf_ciwelsh_cibf_ciTotal0 1 0 1164.5388.5591.34150.5911.450.621315.12  1 110.430.458.66241894.4599.5599.38242994.88  Total 1274.96243395.042560100.00Pooled Variance T-Test versus Behrens DistributionOver same parameters as from the class handout “Pooled and Separate-Variances t-Tests”, and each trial had 975 iterations.Trial 1Trial 2Trial 3Trial 4Trial 5Parameters n.x = 15 n.y = 25 mu.x = 100 mu.y = 100 sg.x = 10 sg.y = 10 n.x = 15 n.y = 25 mu.x = 100 mu.y = 100 sg.x = 10 sg.y = 20 n.x = 15 n.y = 25 mu.x = 100 mu.y = 100 sg.x = 20 sg.y = 10 n.x = 15 n.y = 25 mu.x = 100 mu.y = 120 sg.x = 10 sg.y = 10 n.x = 15 n.y = 25 mu.x = 100 mu.y = 110 sg.x = 10 sg.y = 10Pooled VarianceT-TestMean( p-value < 0.05 )0.042051280.030769230.100512810.84102561-mean(ci)0.042051280.030769230.10051280.055384620.8194872Behrens DistributionMean( p-value < 0.05 )0.042051280.058461540.0543589710.047179491-mean(ci)0.042051280.060512820.054358970.046153850.04205128While the identical results are surprising for trial 1, it is correct. 12 of the 975 iterations had different results, and in 6 of those trials the pooled t test had the right confidence interval, in the other six the Behrens distribution had the better confidence interval. Thinking about this a bit more, it should not be surprising because the pooled variance t test should just be a special case under the Behrens distribution. Still, keep in mind that in this case the trials are simulated less then a thousand times, the original handout specified 10,000 simulations, and so these results are not precise for more then a few decimal places.ConclusionSince the Bayesian book I got most of my information is copyrighted 2004, I assume that the Patil approximation is still currently the best way to calculate the Behrens distribution today. Admittedly, calculating precise results by numerical integration takes a significant amount of time even on current computers. If only a few sets confidence intervals are needed, the patient statistician will get a confidence interval that is more precise then using the Welsh approximation. On the other hand for simulation type takes where thousands of confidence intervals are needed, a trade-off between running time and precision will need to be made. Still, if statistical packages where serious about supporting the Behrens distribution, a Behrens lookup table could be calculated ahead of time to an arbitrary precision and stored on the computer. Thus whenever Behrens quartiles are needed, instead of performing a series of numeric integrations, at most the hard drive could be queried the lookup table in a few milliseconds. Computer packages like SAS are already huge packages and could easily include a detailed enough Behrens lookup table to push the precession to several decimal places.As computer processing power and storage capacities continue to increase, more statisticians and statistical package developers will question the utility of the Welsh approximation. Furthermore, noting how the Behrens distribution handles the equal variance case as a special case (proving this is outside the scope of this project), packages like R would not need parameters like var.equal for t.test().