{"id":2294,"date":"2020-08-01T11:00:00","date_gmt":"2020-08-01T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=2294"},"modified":"2020-07-23T16:26:25","modified_gmt":"2020-07-23T07:26:25","slug":"beta-prime-distribution","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/beta-prime-distribution","title":{"rendered":"\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u30d9\u30fc\u30bf\u30d7\u30e9\u30a4\u30e0\u5206\u5e03\uff09"},"content":{"rendered":"\n\n\n\n\n<p>\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u53cd\u8ee2\u30d9\u30fc\u30bf\u5206\u5e03\u3001beta prime distribution\u3001beta distribution of the second kind\uff09\u306f\u3001\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u78ba\u7387\u5909\u6570\\(X\\)\u304c\uff08\u7b2c\uff11\u7a2e\uff09\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u5f93\u3046\u3068\u304d\\(\\displaystyle\\frac{X}{1-X}\\)\u304c\u5f93\u3046\u5206\u5e03\u304c\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u3067\u3059\u3002\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\)\u306f\u3001\u8a18\u53f7\\(Beta^{\\prime}\\)\u3092\u7528\u3044\u3066\u3001\\(X\\sim Beta^{\\prime}(\\alpha,\\beta)\\)\u3068\u8868\u3055\u308c\u307e\u3059\u3002<br>\u3000\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u306f\u3042\u307e\u308a\u304a\u76ee\u306b\u304b\u304b\u308b\u3053\u3068\u306f\u306a\u3044\u3067\u3059\u304c\u3001\u8a08\u7b97\u4e0a\u77e5\u3063\u3066\u304a\u304f\u3068\u4fbf\u5229\u306a\u3053\u3068\u3082\u3042\u308b\u306e\u3067\u3001\u96d1\u5b66\u7a0b\u5ea6\u306b\u899a\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\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> \u7b2c\uff12\u7a2e\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> \u4e00\u822c\u5316\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03<\/a><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">3<\/span> \u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u57fa\u672c\u6027\u8cea<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_1\">4<\/span> \u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u4ed6\u306e\u5206\u5e03\u3068\u306e\u95a2\u4fc2<\/a><\/li><li><a href=\"#i-6\"><span class=\"toc_number toc_depth_1\">5<\/span> \u7b2c\uff12\u7a2e\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\">\u7b2c\uff12\u7a2e\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: 427px;\">\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 \\)<\/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)^{-\\alpha-\\beta} }{ 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_{\\frac{x}{1+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 \\frac{e^{-t}\\Gamma(\\alpha+\\beta)}{\\Gamma(\\beta)}G_{1,2}^{\\ 2,0}\\left(<br \/>\\begin{array}{c|c}<br \/>\\alpha+\\beta &amp; \\\\<br \/>\\beta,0 &amp; -t<br \/>\\end{array}\\right)\\)<\/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\u306e\u539f\u70b9\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\(\\displaystyle \\prod_{k=1}^{r}\\frac{\\alpha+k-1}{\\beta-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\/mean-definition\">\u671f\u5f85\u5024<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\( \\displaystyle\\frac{\\alpha}{\\beta-1}\\ \\ \\ \uff08\u305f\u3060\u3057\\beta&gt;1\uff09 \\)<\/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(\\alpha+\\beta-1)}{ (\\beta-2)(\\beta-1)^{2} }\\ \\ \\ \uff08\u305f\u3060\u3057\\beta&gt;2\uff09 \\)<\/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 }{ \\beta+1 }\\ \\ \\ \uff08\u305f\u3060\u3057\\alpha\\geq 1\u3067\u3001\u305d\u308c\u4ee5\u5916\u306f0\uff09 \\)<\/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(2\\alpha+\\beta-1)}{\\beta-3}\\sqrt{ \\frac{\\beta-2}{\\alpha(\\alpha+\\beta-1)} }\\ \\ \\ \uff08\u305f\u3060\u3057\\beta&gt;3\uff09\\)<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n\n\n<p>\u305f\u3060\u3057\u3001\\(\\displaystyle G_{1,2}^{\\ 2,0}\\left(<br>\\begin{array}{c|c}<br>\\alpha+\\beta &amp; \\\\<br>\\beta,0 &amp; -t<br>\\end{array}\\right)\\)\u306fMeijer\u306eG\u95a2\u6570\u3067\u3042\u308a<br><div style=\"overflow-x: auto;\">\\begin{align}<br>G_{p,q}^{\\ m,n}\\left(<br>\\begin{array}{c|c}<br>a_{1},\\cdots,a_{p} &amp; \\\\<br>b_{1},\\cdots,b_{q} &amp; z<br>\\end{array}\\right) &amp;= \\frac{1}{2\\pi i}\\int_{L}\\frac{ \\prod_{j=1}^{m}\\Gamma(b_{j}-s)\\prod_{j=1}^{n}\\Gamma(1-a_{j}+s) }{ \\prod_{j=m+1}^{q}\\Gamma(1-b_{j}+s)\\prod_{j=n+1}^{p}\\Gamma(a_{j}-s) }z^{s}ds<br>\\end{align}<\/div><br>\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\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\/cbetapri-mv\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03-100x100.png\" alt=\"\u7b2c\uff12\u7a2e\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\">\u7b2c\uff12\u7a2e\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 \u3000\u3053\u306e\u8a18\u4e8b\u3067\u306f\u7b2c\uff12\u7a2e\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\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\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\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=\"617\" src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03.png\" alt=\"\" class=\"wp-image-2312\" srcset=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03.png 980w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03-300x189.png 300w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03-768x484.png 768w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03-320x201.png 320w\" sizes=\"(max-width: 980px) 100vw, 980px\" \/><\/figure>\n\n\n\n<h2><span id=\"i-3\">\u4e00\u822c\u5316\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03<\/span><\/h2>\n\n\n\n<p>\u3000\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u3055\u3089\u306b\u3001\u5b9f\u6570\\(p,q&gt;0\\)\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u8ffd\u52a0\u3057\u305f\u6b21\u5f0f\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u3001\u4e00\u822c\u5316\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\uff08generalized beta prime distribution\uff09\u3068\u3044\u3044\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>f(x|\\alpha,\\beta,p,q) &amp;= \\frac{ p\\left( \\frac{x}{q} \\right)^{\\alpha p-1}\\left( 1+\\left( \\frac{x}{q} \\right)^{p} \\right)^{-\\alpha-\\beta} }{ qB(\\alpha,\\beta) }<br>\\end{align}<\/div><br>\u30d1\u30e9\u30e1\u30fc\u30bf\\(p=q=1\\)\u306e\u3068\u304d\u3001\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\\(Beta^{\\prime}(\\alpha,\\beta)\\)\u306b\u5f93\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-4\">\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u57fa\u672c\u6027\u8cea<\/span><\/h2>\n\n\n\n<p>\u3000\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u304c\u6301\u3064\u7279\u5fb4\u3092\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002\u6a5f\u4f1a\u304c\u3042\u308c\u3070\u8a3c\u660e\u3082\u3057\u3066\u3044\u304d\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<ul><li>\u78ba\u7387\u5909\u6570\\(X\\)\u304c\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\\(X\\sim Beta^{\\prime}(\\alpha,\\beta)\\)\u306b\u5f93\u3046\u3068\u304d\u3001\u9006\u6570\u3082\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\\(X\\sim Beta^{\\prime}(\\beta,\\alpha)\\)\u306b\u5f93\u3044\u307e\u3059\u3002<br>\u3000<\/li><li>\u78ba\u7387\u5909\u6570\\(X\\)\u304c\u4e00\u822c\u5316\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\\(X\\sim Beta^{\\prime}(\\alpha,\\beta,p,q)\\)\u306b\u5f93\u3046\u3068\u304d\u3001\u30b9\u30ab\u30e9\u30fc\u500d\u3057\u305f\u78ba\u7387\u5909\u6570\u3082\u4e00\u822c\u5316\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\\(kX\\sim Beta^{\\prime}(\\alpha,\\beta,p,kq)\\)\u306b\u5f93\u3044\u307e\u3059\u3002<\/li><\/ul>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-5\">\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u4ed6\u306e\u5206\u5e03\u3068\u306e\u95a2\u4fc2<\/span><\/h2>\n\n\n\n<p>\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u4ed6\u306e\u5206\u5e03\u3068\u306e\u95a2\u4fc2\u3092\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<ul><li>\u78ba\u7387\u5909\u6570\\(X\\)\u304c\\(F\\)\u5206\u5e03\\(X\\sim F(2\\alpha,2\\beta)\\)\u306b\u5f93\u3046\u3068\u304d\u3001\u3053\u306e\u3068\u304d<div style=\"overflow-x: auto;\">\\begin{align}\\frac{\\alpha}{\\beta}X\\sim Beta^{\\prime}(\\alpha,\\beta)\u3082\u3057\u304f\u306fX\\sim Beta^{\\prime}(\\alpha,\\beta,1,\\frac{\\beta}{\\alpha})\\end{align}<\/div>\u3068\u306a\u308a\u307e\u3059\u3002<br>\u3000<\/li><li>\u78ba\u7387\u5909\u6570\\(X\\)\u304c\u30d9\u30fc\u30bf\u5206\u5e03\\(X\\sim Beta(\\alpha,\\beta)\\)\u306b\u5f93\u3046\u3068\u304d\u3001\\(X\/(1-X)\\)\u306f\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03<div style=\"overflow-x: auto;\">\\begin{align}\\frac{X}{1-X}\\sim Beta^{\\prime}(\\alpha,\\beta)\\end{align}<\/div>\u306b\u5f93\u3044\u307e\u3059\u3002<br>\u3000<\/li><li>\u78ba\u7387\u5909\u6570\\(X,Y\\)\u304c\u4e92\u3044\u306b\u72ec\u7acb\u306b\u30ac\u30f3\u30de\u5206\u5e03\\(X\\sim Gam(\\alpha,1),\\ Y\\sim Gam(\\beta,1)\\)\u306b\u5f93\u3063\u3066\u3044\u308b\u3068\u304d\u3001<div style=\"overflow-x: auto;\">\\begin{align}\\frac{X}{Y}\\sim Beta^{\\prime}(\\alpha,\\beta)\\end{align}<\/div>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<br>\u3000<\/li><li>\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\\(\\beta=1\\)\u306e\u3068\u304d\u3001\u78ba\u7387\u5909\u6570\\(X\\sim Beta^{\\prime}(\\alpha,1,p,q)\\)\u306f\u3001Dagum\u5206\u5e03\\(Dagum(\\alpha,p,q)\\)\u3068\u540c\u7b49\u306b\u306a\u308a\u307e\u3059\u3002<br>\u3000<\/li><li>\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\\(\\alpha=1\\)\u306e\u3068\u304d\u3001\u78ba\u7387\u5909\u6570\\(X\\sim Beta^{\\prime}(1,\\beta,p,q)\\)\u306f\u3001Burr\u5206\u5e03\\(SinghMaddala(\\beta,p,q)\\)\u3068\u540c\u7b49\u306b\u306a\u308a\u307e\u3059\u3002<br>\u3000<\/li><li>\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\\(\\alpha=\\beta=1\\)\u306e\u3068\u304d\u3001\u78ba\u7387\u5909\u6570\\(X\\sim Beta^{\\prime}(1,1,p,q)\\)\u306f\u3001\u5bfe\u6570\u30ed\u30b8\u30b9\u30c6\u30a3\u30af\u30b9\u5206\u5e03\\(LL(p,q)\\)\u3068\u540c\u7b49\u306b\u306a\u308a\u307e\u3059\u3002<\/li><\/ul>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-6\">\u7b2c\uff12\u7a2e\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\u7b2c\uff12\u7a2e\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\/beta-distribution\">\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\uff11-100x100.png\" alt=\"\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u7b2c\uff11\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\uff09\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u7b2c\uff11\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\uff09<\/div>\n    <div class=\"blogcard_excerpt\">\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\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\/dirichlet-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=\"\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03<\/div>\n    <div class=\"blogcard_excerpt\">\u3000\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03\uff08Dirichlet distribution\uff09\u306f\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u3092\u591a\u6b21\u5143\u5316\u3057\u305f\u3082\u306e\u306b\u306a\u308a\u307e\u3059\u3002\u3000\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03\u306f\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03\uff08\u53cd\u8ee2\u30d9\u30fc\u30bf\u5206\u5e03\u3001beta prime distribution\u3001beta distribution of the seco &#8230; <\/p>\n","protected":false},"author":1,"featured_media":2312,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[84],"tags":[71,111],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u7b2c\uff12\u7a2e\u30d9\u30fc\u30bf\u5206\u5e03.png","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2294"}],"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=2294"}],"version-history":[{"count":38,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2294\/revisions"}],"predecessor-version":[{"id":2355,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2294\/revisions\/2355"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/2312"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=2294"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=2294"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=2294"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}