{"id":2153,"date":"2020-07-26T11:00:00","date_gmt":"2020-07-26T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=2153"},"modified":"2020-07-22T14:01:54","modified_gmt":"2020-07-22T05:01:54","slug":"beta-distribution","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/beta-distribution","title":{"rendered":"\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u7b2c\uff11\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\uff09"},"content":{"rendered":"\n\n\n\n\n<p>\u3000\u30d9\u30fc\u30bf\u5206\u5e03\uff08beta distribution\uff09\u306f\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u306f\u7b2c\uff11\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u304c\u3042\u308a\u3001\u5358\u306b\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u547c\u3076\u3068\u304d\u306b\u306f\u7b2c\uff11\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002\u30d9\u30fc\u30bf\u5206\u5e03\u306f\u4ed6\u306e\u5206\u5e03\u3068\u305f\u304f\u3055\u3093\u306e\u95a2\u4fc2\u3092\u6301\u3063\u3066\u304a\u308a\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6761\u4ef6\u306b\u3088\u3063\u3066\u306f\u3001\u4e00\u69d8\u5206\u5e03\u3084\u30d9\u30ad\u95a2\u6570\u5206\u5e03\u3001\u30ac\u30f3\u30de\u5206\u5e03\u3001\u30ab\u30a4\uff12\u4e57\u5206\u5e03\u306a\u3069\u306b\u306a\u308a\u307e\u3059\u3002\u3000<br>\u3000\u30d9\u30fc\u30bf\u5206\u5e03\u306f\u3001\u30b3\u30a4\u30f3\u6295\u3052\u306e\u3088\u3046\u306b\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306b\u304a\u3051\u308b\u4e88\u6e2c\u5206\u5e03\u3068\u3057\u3066\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3088\u308a\u6b63\u78ba\u306b\u306f\u3001\u4e8b\u524d\u5206\u5e03\u304c\u4e00\u69d8\u5206\u5e03\u3001\u5c24\u5ea6\u304c\uff12\u9805\u5206\u5e03\u306e\u3068\u304d\u306b\u4e8b\u5f8c\u5206\u5e03\u304c\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<div id=\"toc_container\" class=\"toc_light_blue no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u30d9\u30fc\u30bf\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831<\/a><ul><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_2\">1.1<\/span> \u78ba\u7387\u5bc6\u5ea6\u95a2\u6570<\/a><\/li><\/ul><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">2<\/span> \u30d9\u30fc\u30bf\u5206\u5e03\u3092\u8003\u3048\u308b\u4e0a\u3067\u306e\u57fa\u790e\u77e5\u8b58<\/a><ul><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_2\">2.1<\/span> \u30d9\u30fc\u30bf\u95a2\u6570\u3068\u30ac\u30f3\u30de\u95a2\u6570<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_2\">2.2<\/span> \u30d9\u30fc\u30bf\u95a2\u6570\u306e\u57fa\u672c\u6027\u8cea<\/a><\/li><li><a href=\"#i-6\"><span class=\"toc_number toc_depth_2\">2.3<\/span> \u30ac\u30f3\u30de\u95a2\u6570\u306e\u57fa\u672c\u6027\u8cea<\/a><\/li><\/ul><\/li><li><a href=\"#i-7\"><span class=\"toc_number toc_depth_1\">3<\/span> \u30d9\u30fc\u30bf\u5206\u5e03\u65cf<\/a><\/li><li><a href=\"#i-8\"><span class=\"toc_number toc_depth_1\">4<\/span> \u30d9\u30fc\u30bf\u5206\u5e03\u3068\u4ed6\u306e\u5206\u5e03\u3068\u306e\u95a2\u4fc2<\/a><ul><li><a href=\"#i-9\"><span class=\"toc_number toc_depth_2\">4.1<\/span> \u4e00\u69d8\u5206\u5e03<\/a><\/li><li><a href=\"#i-10\"><span class=\"toc_number toc_depth_2\">4.2<\/span> \u30d9\u30ad\u95a2\u6570\u5206\u5e03<\/a><\/li><li><a href=\"#i-11\"><span class=\"toc_number toc_depth_2\">4.3<\/span> \uff12\u9805\u5206\u5e03<\/a><\/li><li><a href=\"#F\"><span class=\"toc_number toc_depth_2\">4.4<\/span> \\(F\\)\u5206\u5e03<\/a><\/li><li><a href=\"#i-12\"><span class=\"toc_number toc_depth_2\">4.5<\/span> \u30ac\u30f3\u30de\u5206\u5e03<\/a><\/li><li><a href=\"#i-13\"><span class=\"toc_number toc_depth_2\">4.6<\/span> \u30ab\u30a4\uff12\u4e57\u5206\u5e03<\/a><\/li><li><a href=\"#i-14\"><span class=\"toc_number toc_depth_2\">4.7<\/span> \u6a19\u6e96\u6b63\u898f\u5206\u5e03<\/a><\/li><\/ul><\/li><li><a href=\"#i-15\"><span class=\"toc_number toc_depth_1\">5<\/span> \u30d9\u30fc\u30bf\u5206\u5e03\u3068\u95a2\u9023\u6df1\u3044\u4ed6\u306e\u5206\u5e03\u3068\u306e\u95a2\u4fc2<\/a><\/li><\/ul><\/div>\n<h2><span id=\"i\">\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831<\/span><\/h2>\n\n\n\n<p>\u203b\u3000\u8868\u306f\u6a2a\u306b\u30b9\u30af\u30ed\u30fc\u30eb\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n<figure class=\"wp-block-table\">\n<table style=\"width: 100%; height: 523px;\">\n<tbody>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\">\u30d1\u30e9\u30e1\u30fc\u30bf<\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\(0 &lt; \\alpha,\\ \\ \\ 0 &lt; \\beta\\)<\/td>\n<\/tr>\n<tr style=\"height: 56px;\">\n<td style=\"width: 17.5862%; height: 56px;\">\u78ba\u7387\u5909\u6570\u306e\u7bc4\u56f2<\/td>\n<td style=\"width: 82.2414%; height: 56px;\">\\(0\\leq x \\leq 1\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/probability-function\">\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\(\\displaystyle\\frac{ x^{\\alpha-1}(1-x)^{\\beta-1} }{ B(\\alpha,\\beta) }\\)<br \/>\u305f\u3060\u3057\u3001\\(B(\\alpha,\\beta)\\)\u306f\u30d9\u30fc\u30bf\u95a2\u6570\u3067\u3059\u3002<br \/>\\(\\displaystyle B(\\alpha,\\beta) = \\int_{0}^{1}u^{\\alpha-1}(1-u)^{\\beta-1}du\\)<\/td>\n<\/tr>\n<tr style=\"height: 56px;\">\n<td style=\"width: 17.5862%; height: 56px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cumulative-distribution-function\">\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/a><\/td>\n<td style=\"width: 82.2414%; height: 56px;\">\\(\\displaystyle I_{x}(\\alpha,\\beta)\\)<br \/>\u305f\u3060\u3057\u3001\\(\\displaystyle I_{x}(\\alpha,\\beta)\\)\u306f\u4e0d\u5b8c\u5168\u30d9\u30fc\u30bf\u95a2\u6570\u6bd4\u3067\u3059\u3002<br \/>\u4e0d\u5b8c\u5168\u30d9\u30fc\u30bf\u95a2\u6570\u3067\u306f\u306a\u3044\u306e\u3067\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002<br \/>\\(\\displaystyle I_{x}(\\alpha,\\beta) = \\frac{1}{B(\\alpha,\\beta) }\\int_{0}^{x}u^{\\alpha-1}(1-u)^{\\beta-1}du\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mgf\">\u7a4d\u7387\u6bcd\u95a2\u6570<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\(\\displaystyle 1+\\sum_{k=1}^{\\infty}\\left( \\prod_{r=0}^{k-1}\\frac{\\alpha+r}{\\alpha+\\beta+r} \\right)\\frac{t^{k}}{k!} \\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cf\">\u7279\u6027\u95a2\u6570<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\(\\displaystyle _{1}\\!F_{1}(\\alpha,\\alpha+\\beta;it) =1+\\sum_{k=1}^{\\infty}\\left( \\prod_{r=0}^{k-1}\\frac{\\alpha+r}{\\alpha+\\beta+r} \\right)\\frac{(it)^{k}}{k!}\\)<br \/>\u305f\u3060\u3057\u3001\\(_{1}F_{1}(\\alpha,\\alpha+\\beta;it)\\)\u306f\u5408\u6d41\u578b\u8d85\u5e7e\u4f55\u95a2\u6570\u3067\u6b21\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002<br \/>\\(\\displaystyle\u00a0 _{1}F_{1}(a,b;z)=\\frac{1}{B(a,b)}\\int_{0}^{1}e^{zt}t^{a-1}(1-t)^{b-a-1}dt\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/moment\">\\(r\\)\u6b21\u30e2\u30fc\u30e1\u30f3\u30c8<\/a><br \/>\uff08\u539f\u70b9\u307e\u308f\u308a\uff09<\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\(\\displaystyle\\prod_{j=0}^{r-1}\\frac{\\alpha+j}{\\alpha+\\beta+j}=\\frac{B(\\alpha+r,\\beta)}{B(\\alpha,\\beta)}=\\frac{\\Gamma(\\alpha+r)\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)\\Gamma(\\alpha+\\beta+r)}\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 31px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/moment\"><span id=\"MathJax-Element-10-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-229\" class=\"math\"><span id=\"MathJax-Span-230\" class=\"mrow\"><span id=\"MathJax-Span-231\" class=\"mi\">r<\/span><\/span><\/span><\/span>\u6b21\u30e2\u30fc\u30e1\u30f3\u30c8<\/a><br \/>\uff08\u5e73\u5747\u307e\u308f\u308a\uff09<\/td>\n<td style=\"width: 82.2414%; height: 31px;\">\\(\\lambda=(\\alpha+\\beta)^{-1},\\ \\ \\theta=\\alpha(\\alpha+\\beta)^{-1}\\)\u3068\u304a\u304f\u3068\u3001\\(r\\)\u6b21\u306e\u5e73\u5747\u307e\u308f\u308a\u306e<br \/>\u30e2\u30fc\u30e1\u30f3\u30c8\\(\\mu_{r}\\)\u306b\u95a2\u3057\u3066\u3001\u6b21\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<br \/>\\(\\displaystyle \\mu_{r+1} =\\frac{ r\\lambda }{ 1+r\\lambda }\\mu_{r}+\\theta\\sum_{j=1}^{r}\\ _{r}C_{j}\\frac{\\lambda^{j}(1-\\theta)^{j}j!}{(1+r\\lambda)\\cdots\\{1+(r-j)\\lambda\\}}\\mu_{r-j} \\)<br \/>\\(\\mu_{0}=1,\\ \\ \\ \\mu_{1}=0\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition\">\u671f\u5f85\u5024<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\( \\displaystyle\\frac{\\alpha}{\\alpha+\\beta} \\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/variance\">\u5206\u6563<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\( \\displaystyle\\frac{\\alpha\\beta}{(\\alpha+\\beta)^{2}(\\alpha+\\beta+1)} \\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 35px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/05231022\">\u30e2\u30fc\u30c9<\/a><\/td>\n<td style=\"width: 82.2414%; height: 35px;\">\\( \\displaystyle\\frac{\\alpha-1}{\\alpha+\\beta-2},\\ \\ \\alpha &gt; 1,\\ \\ \\beta &gt; 1 \\)<\/td>\n<\/tr>\n<tr style=\"height: 100px;\">\n<td style=\"width: 17.5862%; height: 100px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/skewness\">\u6b6a\u5ea6<\/a><\/td>\n<td style=\"width: 82.2414%; height: 100px;\">\n<p>\\(\\displaystyle \\frac{2(\\beta-\\alpha)(\\alpha+\\beta+1)^{\\frac{1}{2}}}{(\\alpha+\\beta+2)(\\alpha\\beta)^{\\frac{1}{2}}}\\)<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 29px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/kurtosis\">\u5c16\u5ea6<\/a><\/td>\n<td style=\"width: 82.2414%; height: 29px;\">\\(\\displaystyle\\frac{3(\\alpha+\\beta)(\\alpha+\\beta+1)(\\beta+1)(2\\beta-\\alpha)}{\\alpha\\beta(\\alpha+\\beta+2)(\\alpha+\\beta+3)}+\\frac{\\alpha(\\alpha-\\beta)}{\\alpha+\\beta} \\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n\n\n<h3>\u8a3c\u660e\u4e00\u89a7<\/h3>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cbetad-mv\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff12-100x100.png\" alt=\"\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011<\/div>\n    <div class=\"blogcard_excerpt\">\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2605\u2605\u2606\u2606 \u3053\u306e\u8a18\u4e8b\u3067\u306f\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u3092\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9\u304c\u5206\u304b\u3089\u306a\u3044\u65b9\u306f\u662f\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cbetad-mgf\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff13-100x100.png\" alt=\"\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011<\/div>\n    <div class=\"blogcard_excerpt\">\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2605\u2605\u2606\u2606 \u3053\u306e\u8a18\u4e8b\u3067\u306f\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u3092\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u7a4d\u7387\u6bcd\u95a2\u6570\u306e\u6c42\u3081\u65b9\u304c\u5206\u304b\u3089\u306a\u3044\u65b9\u306f\u662f\u975e\u304a\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cbetad-cf\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff13-100x100.png\" alt=\"\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u7279\u6027\u95a2\u6570\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u7279\u6027\u95a2\u6570\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011<\/div>\n    <div class=\"blogcard_excerpt\">\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2605\u2605\u2606\u2606 \u3053\u306e\u8a18\u4e8b\u3067\u306f\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u7279\u6027\u95a2\u6570\u3092\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u7279\u6027\u95a2\u6570\u306e\u6c42\u3081\u65b9\u304c\u5206\u304b\u3089\u306a\u3044\u65b9\u306f\u662f\u975e\u304a\u8aad\u307f\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n<h3><span id=\"i-2\">\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570<\/span><\/h3>\n\n\n\n<p>\u69d8\u3005\u306a\\(\\alpha,\\beta\\)\u306b\u5bfe\u5fdc\u3059\u308b\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<br>\u30fb\\(\\alpha &gt; 0,\\beta &gt;0\\)\u306e\u3068\u304d\u3001\\((\\alpha-1)\/(\\alpha+\\beta-2)\\)\u3067\u6700\u5c0f\u5024\u3092\u3068\u308a\u3001\u95a2\u6570\u306e\u5f62\u306f\\(U\\)\u5b57\u578b\u306b\u306a\u308a\u307e\u3059\u3002<br>\u30fb\\(\\alpha &lt; 1,\\beta &lt;1\\)\u306e\u3068\u304d\u3001\\((\\alpha-1)\/(\\alpha+\\beta-2)\\)\u3067\u5358\u4e00\u306e\u30e2\u30fc\u30c9\u3092\u3068\u308a\u307e\u3059\u3002<br>\u30fb\\(\\alpha =\\beta\\)\u306e\u3068\u304d\u3001\\(1\/2\\)\u3092\u4e2d\u5fc3\u306b\u5bfe\u79f0\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"980\" height=\"618\" src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff11.png\" alt=\"\" class=\"wp-image-2174\" srcset=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff11.png 980w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff11-300x189.png 300w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff11-768x484.png 768w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff11-320x202.png 320w\" sizes=\"(max-width: 980px) 100vw, 980px\" \/><\/figure>\n\n\n\n<p>\\(\\alpha=2\\)\u3067\u56fa\u5b9a\u3057\u305f\u5834\u5408\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<br>\u30fb\\((\\alpha-1)(\\beta-1) \\leq 0\\)\u306e\u3068\u304d\u3001\u95a2\u6570\u306f\u6700\u5c0f\u5024\u3092\u6301\u305f\u305a\u3001\u95a2\u6570\u306e\u5f62\u306f\\(J\\)\u5b57\u578b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"980\" height=\"618\" src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff12.png\" alt=\"\" class=\"wp-image-2175\" srcset=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff12.png 980w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff12-300x189.png 300w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff12-768x484.png 768w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff12-320x202.png 320w\" sizes=\"(max-width: 980px) 100vw, 980px\" \/><\/figure>\n\n\n\n<p>\\(\\beta=4\\)\u3067\u56fa\u5b9a\u3057\u305f\u5834\u5408\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"980\" height=\"618\" src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff13.png\" alt=\"\" class=\"wp-image-2176\" srcset=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff13.png 980w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff13-300x189.png 300w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff13-768x484.png 768w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff13-320x202.png 320w\" sizes=\"(max-width: 980px) 100vw, 980px\" \/><\/figure>\n\n\n\n<h2><span id=\"i-3\">\u30d9\u30fc\u30bf\u5206\u5e03\u3092\u8003\u3048\u308b\u4e0a\u3067\u306e\u57fa\u790e\u77e5\u8b58<\/span><\/h2>\n\n\n\n<p>(1)\u30d9\u30fc\u30bf\u95a2\u6570<br><div style=\"overflow-x: auto;\">\\begin{align}<br>B(\\alpha,\\beta) = \\int_{0}^{1}u^{\\alpha-1}(1-u)^{\\beta-1}du,\\ \\ \\ 0\\leq u\\leq 1<br>\\end{align}<\/div><\/p>\n\n\n\n<p>(2)\u30ac\u30f3\u30de\u95a2\u6570<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\Gamma(a) = \\int_{0}^{\\infty}\\exp[-u]u^{a-1}du,\\ \\ \\ a&gt;0<br>\\end{align}<\/div><\/p>\n\n\n\n<p>(3)\u30c7\u30a3\u30ac\u30f3\u30de\u95a2\u6570\uff08\u30d7\u30b5\u30a4\u95a2\u6570\uff09<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\psi(a) = \\frac{d}{da}\\log\\Gamma(a) = \\frac{\\displaystyle\\frac{d\\Gamma(a)}{da}}{\\Gamma(a)}<br>\\end{align}<\/div><\/p>\n\n\n\n<h3><span id=\"i-4\">\u30d9\u30fc\u30bf\u95a2\u6570\u3068\u30ac\u30f3\u30de\u95a2\u6570<\/span><\/h3>\n\n\n\n<p>\u30d9\u30fc\u30bf\u95a2\u6570\u3068\u30ac\u30f3\u30de\u95a2\u6570\u306b\u306f\u6b21\u306e\u3088\u3046\u306a\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>B(\\alpha,\\beta)=\\frac{\\Gamma(\\alpha)\\Gamma(\\beta)}{\\Gamma(\\alpha+\\beta)} = B(\\beta,\\alpha)<br>\\end{align}<\/div><\/p>\n\n\n\n<h3><span id=\"i-5\">\u30d9\u30fc\u30bf\u95a2\u6570\u306e\u57fa\u672c\u6027\u8cea<\/span><\/h3>\n\n\n\n<p>\u30d9\u30fc\u30bf\u95a2\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6027\u8cea\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>B(\\alpha+1,\\beta)=\\frac{\\alpha}{\\alpha+\\beta}B(\\alpha,\\beta)<br>\\end{align}<\/div><br>\u7279\u306b\\(\\alpha,\\beta\\)\u304c\u6574\u6570\u306e\u3068\u304d\u3001\u6b21\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>B(\\alpha,\\beta) &amp;= \\frac{(\\alpha-1)!(\\beta-1)!}{(\\alpha+\\beta-1)!} \\\\<br>B(1,1) &amp;= 1\\\\<br>B\\left( \\frac{1}{2},\\frac{1}{2} \\right) &amp;= \\pi<br>\\end{align}<\/div><\/p>\n\n\n\n<h3><span id=\"i-6\">\u30ac\u30f3\u30de\u95a2\u6570\u306e\u57fa\u672c\u6027\u8cea<\/span><\/h3>\n\n\n\n<p>\u30ac\u30f3\u30de\u95a2\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6027\u8cea\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\Gamma(a)=(a-1)\\Gamma(a-1)<br>\\end{align}<\/div><br>\u7279\u306b\\(a\\)\u304c\u6574\u6570\u306e\u3068\u304d\u3001\u6b21\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\Gamma(a) &amp;= (a-1)! \\\\<br>\\Gamma(0) &amp;= 1 \\\\<br>\\Gamma(1) &amp;= 1 \\\\<br>\\Gamma\\left( \\frac{1}{2} \\right) &amp;= \\sqrt{\\pi} \\\\<br>\\Gamma\\left( a+\\frac{1}{2} \\right) &amp;= \\frac{(2a)!\\sqrt{\\pi}}{a!2^{2a}}<br>\\end{align}<\/div><\/p>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-7\">\u30d9\u30fc\u30bf\u5206\u5e03\u65cf<\/span><\/h2>\n\n\n\n<p>\u30d9\u30fc\u30bf\u5206\u5e03\u65cf\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u6b21\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\frac{1}{B(\\alpha,\\beta)}\\frac{(y-a)^{\\alpha-1}(b-y)^{\\beta-1}}{(b-a)^{\\alpha+\\beta-1}},\\ \\ \\ a\\leq y \\leq b,\\ \\ \\alpha >0,\\ \\ \\beta >0<br>\\end{align}<\/div><br>\u3068\u304f\u306b\u3001\\(\\beta=1\\)\u306e\u3068\u304d\u30d9\u30ad\u95a2\u6570\u5206\u5e03\u3068\u547c\u3070\u308c\u307e\u3059\u3002<br>\u3000\u5909\u6570\\(X\\)\u3092<br><div style=\"overflow-x: auto;\">\\begin{align}<br>X=\\frac{Y-1}{b-a}<br>\\end{align}<\/div><br>\u3067\u7f6e\u304d\u63db\u3048\u308b\u3068\u3001\\(X\\)\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u6a19\u6e96\u5f62<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\frac{ x^{\\alpha-1}(1-x)^{\\beta-1} }{ B(\\alpha,\\beta) }<br>\\end{align}<\/div><br>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-8\">\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u4ed6\u306e\u5206\u5e03\u3068\u306e\u95a2\u4fc2<\/span><\/h2>\n\n\n\n<h3><span id=\"i-9\">\u4e00\u69d8\u5206\u5e03<\/span><\/h3>\n\n\n\n<p>\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\sim Beta(1,1)\\)\u306f\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3044\u307e\u3059\u3002<\/p>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/continuous-uniform-distribution\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09-100x100.png\" alt=\"\u4e00\u69d8\u5206\u5e03\uff08\u9023\u7d9a\u578b\uff09\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u4e00\u69d8\u5206\u5e03\uff08\u9023\u7d9a\u578b\uff09<\/div>\n    <div class=\"blogcard_excerpt\">\u4e00\u69d8\u5206\u5e03\uff08uniform distribution\uff09\u306f\u6700\u3082\u30b7\u30f3\u30d7\u30eb\u306a\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u4e00\u69d8\u5206\u5e03\u306f\u5225\u540d\u3001\u77ed\u5f62\u5206\u5e03\uff08rectangular di\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n<h3><span id=\"i-10\">\u30d9\u30ad\u95a2\u6570\u5206\u5e03<\/span><\/h3>\n\n\n\n<p>\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\sim Beta(1,\\beta)\\)\u306f\u30d9\u30ad\u95a2\u6570\u5206\u5e03\u306b\u5f93\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3><span id=\"i-11\">\uff12\u9805\u5206\u5e03<\/span><\/h3>\n\n\n\n<p>\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\sim Beta(i,n-1+1)\\)\uff08\\(n,i\\)\u306f\u6b63\u306e\u6574\u6570\uff09\u3068\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\\(n,p\\)\u306e\uff12\u9805\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(Y\\sim Bin(n,p)\\)\u306b\u306f\u6b21\u306e\u3088\u3046\u306a\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\mathrm{P}(X\\leq p) = \\mathrm{P}(Y\\geq i)<br>\\end{align}<\/div><\/p>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/binomial-distribution\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\uff12\u9805\u5206\u5e03\uff08\u78ba\u7387\u95a2\u6570-n10\uff09-100x100.png\" alt=\"\uff12\u9805\u5206\u5e03\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\uff12\u9805\u5206\u5e03<\/div>\n    <div class=\"blogcard_excerpt\">\uff12\u9805\u5206\u5e03\uff08binomial distribution\uff09\u306f\u96e2\u6563\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3092\u8907\u6570\u56de\u884c\u3063\u305f\u969b\u306b\u5f97\u3089\u308c\u308b\u30c7\u30fc\u30bf\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u6210\u529f\u78ba\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n<h3><span id=\"F\">\\(F\\)\u5206\u5e03<\/span><\/h3>\n\n\n\n<p>\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\sim Beta(\\frac{\\alpha}{2},\\frac{\\beta}{2})\\)\u3068\u3001\\(F\\)\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(Y\\sim F(\\beta,\\alpha)\\)\u306b\u306f\u6b21\u306e\u3088\u3046\u306a\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\mathrm{P}\\left( X\\leq \\frac{\\alpha}{\\alpha+\\beta x} \\right)=\\mathrm{P}(Y &gt; x)<br>\\end{align}<\/div><\/p>\n\n\n\n<h3><span id=\"i-12\">\u30ac\u30f3\u30de\u5206\u5e03<\/span><\/h3>\n\n\n\n<p>\u30d1\u30e9\u30e1\u30fc\u30bf\\(p,q\\)\u3092\u7528\u3044\u305f\u30ac\u30f3\u30de\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u306f\u3001\u4efb\u610f\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\alpha &gt;0\\)\u3092\u7528\u3044\u305f\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u6b21\u306e\u3088\u3046\u306a\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>Beta(p,q) &amp;= \\frac{ Gam(p,\\alpha) }{ Gam(p,\\alpha)+Gam(q,\\alpha) }<br>\\end{align}<\/div><\/p>\n\n\n\n<h3><span id=\"i-13\">\u30ab\u30a4\uff12\u4e57\u5206\u5e03<\/span><\/h3>\n\n\n\n<p>\u78ba\u7387\u5909\u6570\\(X_{1},X_{2}\\)\u3092\u4e92\u3044\u306b\u72ec\u7acb\u306b\u3001\u81ea\u7531\u5ea6\\(m_{1},m_{2}\\)\u306e\u30ab\u30a4\uff12\u4e57\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3053\u3068\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\frac{X_{1}}{X_{1}+X_{2}}\\sim Beta\\left( \\frac{m_{1}}{2},\\frac{m_{2}}{2} \\right)<br>\\end{align}<\/div><\/p>\n\n\n\n<h3><span id=\"i-14\">\u6a19\u6e96\u6b63\u898f\u5206\u5e03<\/span><\/h3>\n\n\n\n<p>\\(\\frac{\\alpha}{\\beta}\\)\u3092\u4e00\u5b9a\u306b\u4fdd\u3061\u306a\u304c\u3089\u3001\\(\\alpha\\rightarrow\\infty\\),\\(\\beta\\rightarrow\\infty\\)\u3068\u306a\u308b\u3068\u304d\u3001\\(Beta(\\alpha,\\beta)\\)\u306f\u6a19\u6e96\u6b63\u898f\u5206\u5e03\\(N(0,1)\\)\u306b\u53ce\u675f\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-15\">\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u95a2\u9023\u6df1\u3044\u4ed6\u306e\u5206\u5e03\u3068\u306e\u95a2\u4fc2<\/span><\/h2>\n\n\n\n<p>\u3000\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u95a2\u4fc2\u306e\u6df1\u3044\u3068\u3053\u308d\u306b\u3042\u308b\u3001\u5206\u5e03\u3092\u307e\u3068\u3081\u307e\u3057\u305f\u3002\u30a4\u30e1\u30fc\u30b8\u4f5c\u308a\u306b\u3069\u3046\u305e\u3002<br>\u3000\u5404\u5206\u5e03\u306b\u3064\u3044\u3066\u306f\u4e0b\u306e\u30ea\u30f3\u30af\u304b\u3089\u304a\u9858\u3044\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"658\" height=\"412\" src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u95a2\u3059\u308b\u95a2\u4fc2\u56f3.png\" alt=\"\" class=\"wp-image-2193\" srcset=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u95a2\u3059\u308b\u95a2\u4fc2\u56f3.png 658w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u95a2\u3059\u308b\u95a2\u4fc2\u56f3-300x188.png 300w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u95a2\u3059\u308b\u95a2\u4fc2\u56f3-320x200.png 320w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/><\/figure>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/continuous-uniform-distribution\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09-100x100.png\" alt=\"\u4e00\u69d8\u5206\u5e03\uff08\u9023\u7d9a\u578b\uff09\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u4e00\u69d8\u5206\u5e03\uff08\u9023\u7d9a\u578b\uff09<\/div>\n    <div class=\"blogcard_excerpt\">\u4e00\u69d8\u5206\u5e03\uff08uniform distribution\uff09\u306f\u6700\u3082\u30b7\u30f3\u30d7\u30eb\u306a\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u4e00\u69d8\u5206\u5e03\u306f\u5225\u540d\u3001\u77ed\u5f62\u5206\u5e03\uff08rectangular di\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/bernoulli-distribution\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/05\/PAK39_toumeinadice_TP_V-100x100.jpg\" alt=\"\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03<\/div>\n    <div class=\"blogcard_excerpt\">\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03(Bernoulli distribution)\u306f\u96e2\u6563\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3001\uff11\u56de\u306e\u8a66\u884c\u306b\u5bfe\u3057\u3066\u6210\u529f\u30fb\u5931\u6557\u306e\u3044\u305a\u308c\u304b\u304c\u8d77\u3053\u308b\u4e8b\u8c61\u306b\u7528\u3044\u3089\u308c\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/binomial-distribution\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\uff12\u9805\u5206\u5e03\uff08\u78ba\u7387\u95a2\u6570-n10\uff09-100x100.png\" alt=\"\uff12\u9805\u5206\u5e03\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\uff12\u9805\u5206\u5e03<\/div>\n    <div class=\"blogcard_excerpt\">\uff12\u9805\u5206\u5e03\uff08binomial distribution\uff09\u306f\u96e2\u6563\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3092\u8907\u6570\u56de\u884c\u3063\u305f\u969b\u306b\u5f97\u3089\u308c\u308b\u30c7\u30fc\u30bf\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u6210\u529f\u78ba\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n","protected":false},"excerpt":{"rendered":"<p>\u3000\u30d9\u30fc\u30bf\u5206\u5e03\uff08beta distribution\uff09\u306f\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u306f\u7b2c\uff11\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u304c\u3042\u308a\u3001\u5358\u306b\u30d9\u30fc\u30bf &#8230; <\/p>\n","protected":false},"author":1,"featured_media":2174,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[84],"tags":[109,71],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09\uff11.png","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2153"}],"collection":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/comments?post=2153"}],"version-history":[{"count":43,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2153\/revisions"}],"predecessor-version":[{"id":2249,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2153\/revisions\/2249"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/2174"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=2153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=2153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=2153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}