{"id":213,"date":"2023-08-04T02:39:23","date_gmt":"2023-08-04T02:39:23","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e3%83%98%e3%82%99%e3%83%bc%e3%82%bf%e7%89%88%e3%81%ae%e9%85%8d%e5%b8%83\/"},"modified":"2023-08-04T02:39:23","modified_gmt":"2023-08-04T02:39:23","slug":"%e3%83%98%e3%82%99%e3%83%bc%e3%82%bf%e7%89%88%e3%81%ae%e9%85%8d%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e3%83%98%e3%82%99%e3%83%bc%e3%82%bf%e7%89%88%e3%81%ae%e9%85%8d%e5%b8%83\/","title":{"rendered":"\u30d9\u30fc\u30bf\u7248\u306e\u914d\u5e03"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u30d9\u30fc\u30bf\u7248\u914d\u5e03\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u7528\u9014\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u30b0\u30e9\u30d5\u3068\u3053\u306e\u30bf\u30a4\u30d7\u306e\u78ba\u7387\u5206\u5e03\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3092\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-beta\"><\/span>\u30d9\u30fc\u30bf\u7248\u306e\u914d\u5e03\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u30d9\u30fc\u30bf\u5206\u5e03\u306f\u3001<\/strong>\u533a\u9593 (0,1) \u3067\u5b9a\u7fa9\u3055\u308c\u30012 \u3064\u306e\u6b63\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc \u03b1 \u3068 \u03b2 \u306b\u3088\u3063\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u5316\u3055\u308c\u305f\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u5024\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u03b1\u3068\u03b2\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u4e3b\u306a\u7279\u5fb4\u306f\u3001\u305d\u306e\u5f62\u72b6\u304c\u30d1\u30e9\u30e1\u30fc\u30bf \u03b1 \u3068 \u03b2 \u306b\u3088\u3063\u3066\u5236\u5fa1\u3067\u304d\u308b\u3053\u3068\u3067\u3059\u3002\u3055\u3089\u306b\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u306f\u3001\u5024\u304c 0 \u304b\u3089 1 \u307e\u3067\u306e\u78ba\u7387\u5909\u6570\u3092\u5b9a\u7fa9\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u9023\u7d9a\u78ba\u7387\u5909\u6570\u304c\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u3088\u3063\u3066\u652f\u914d\u3055\u308c\u308b\u3053\u3068\u3092\u793a\u3059\u8868\u8a18\u6cd5\u304c\u3044\u304f\u3064\u304b\u3042\u308a\u307e\u3059\u304c\u3001\u6700\u3082\u4e00\u822c\u7684\u306a\u3082\u306e\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ee1d0d8a1624a017b8ef9ce8a67c694e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex]X\\sim Beta(\\alpha,\\beta)\\\\[2ex]X\\sim \\beta_{\\alpha,\\beta}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"121\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7d71\u8a08\u3067\u306f\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u306f\u975e\u5e38\u306b\u591a\u69d8\u306a\u7528\u9014\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u30b5\u30f3\u30d7\u30eb\u306e\u30d1\u30fc\u30bb\u30f3\u30c6\u30fc\u30b8\u306e\u5909\u52d5\u3092\u8abf\u3079\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u30d7\u30ed\u30b8\u30a7\u30af\u30c8\u7ba1\u7406\u3067\u306f\u3001Pert \u5206\u6790\u3092\u5b9f\u884c\u3059\u308b\u305f\u3081\u306b\u30d9\u30fc\u30bf\u914d\u5e03\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-beta\"><\/span>\u30d9\u30fc\u30bf\u5206\u5e03\u30d7\u30ed\u30c3\u30c8<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u5b9a\u7fa9\u3092\u8003\u616e\u3057\u3066\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u3068\u78ba\u7387\u5206\u5e03\u95a2\u6570\u3092\u4ee5\u4e0b\u306b\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0b\u306b\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u30b0\u30e9\u30d5\u304c\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc \u03b1 \u3068 \u03b2 \u306b\u5fdc\u3058\u3066\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u793a\u3057\u307e\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-graphique-beta.png\" alt=\"\u30d9\u30fc\u30bf\u5206\u5e03\u56f3\" class=\"wp-image-4315\" width=\"621\" height=\"372\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u540c\u69d8\u306b\u3001\u4ee5\u4e0b\u3067\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc \u03b1 \u3068 \u03b2 \u306b\u57fa\u3065\u304f\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\u306e\u30b0\u30e9\u30d5\u8868\u793a\u3092\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-beta-cumulative.png\" alt=\"\u7d2f\u7a4d\u30d9\u30fc\u30bf\u5206\u5e03\u56f3\" class=\"wp-image-4316\" width=\"621\" height=\"373\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-beta\"><\/span>\u30d9\u30fc\u30bf\u7248\u30c7\u30a3\u30b9\u30c8\u30ea\u30d3\u30e5\u30fc\u30b7\u30e7\u30f3\u306e\u7279\u5fb4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u30d9\u30fc\u30bf\u7248\u30c7\u30a3\u30b9\u30c8\u30ea\u30d3\u30e5\u30fc\u30b7\u30e7\u30f3\u306e\u6700\u3082\u91cd\u8981\u306a\u7279\u5fb4\u304c\u4f55\u304b\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf \u03b1 \u3068 \u03b2 \u306f\u3001\u5b9f\u6570\u306e\u6b63\u306e\u6570\u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-442bebaba847543d6db71cdf0127a4b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\alpha >0\\\\[2ex] \\beta >0\\end{array}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;54&#8243; width=&#8221;44&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u9818\u57df\u306e\u7bc4\u56f2\u306f 0 \u304b\u3089 1 \u3067\u3042\u308a\u30012 \u3064\u306e\u6975\u7aef\u306a\u5024\u306f\u542b\u307e\u308c\u307e\u305b\u3093\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-60f8667881e2c5a08eae2db3c3e04708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u5e73\u5747\u306f\u3001\u30a2\u30eb\u30d5\u30a1\u3092\u30a2\u30eb\u30d5\u30a1\u3068\u30d9\u30fc\u30bf\u306e\u5408\u8a08\u3067\u5272\u3063\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4530a8b72211111e8bec79b6388e00a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex] E[X]=\\cfrac{\\alpha}{\\alpha+\\beta}\\end{array} \" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"111\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u5206\u6563\u306f\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-71c6ef40db833722e63c56cd763d6601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex] Var(X)=\\cfrac{\\alpha\\cdot \\beta}{(\\alpha+\\beta+1)\\cdot (\\alpha+\\beta)^2}\\end{array} \" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30a2\u30eb\u30d5\u30a1\u3068\u30d9\u30fc\u30bf\u306e\u5024\u304c 1 \u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u30e2\u30fc\u30c9\u306f\u6b21\u306e\u5f0f\u3067\u7c21\u5358\u306b\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-472cafc0cf9d1cf782206ddc7c9475d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=\\cfrac{\\alpha-1}{\\alpha+\\beta-2}\\qquad \\alpha,\\beta>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;42&#8243; width=&#8221;225&#8243; style=&#8221;vertical-align: -16px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-48f1f2a13df23d7c779bc37da4b49368_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{x^{\\alpha-1}(1-x)^{\\beta-1}}{B(\\alpha,\\beta)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"218\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001B(\u03b1,\u03b2) \u306f\u30d9\u30fc\u30bf\u95a2\u6570\u3067\u3042\u308a\u3001\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f4eb1d2659d9993f9d05a35cce63fc14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B(\\alpha,\\beta)=\\int_0^1x^{\\alpha-1}(1-x)^{\\beta-1}dx\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"248\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\u95a2\u6570\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-031b21ea3e2964d3ac4e6f222356d55b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{B(x;\\alpha,\\beta)}{B(\\alpha,\\beta)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"176\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001B(x;\u03b1,\u03b2) \u306f\u4e0d\u5b8c\u5168\u30d9\u30fc\u30bf\u95a2\u6570\u3067\u3042\u308a\u3001\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6c64764f48f86e8f97df5ed1e8d7fbe6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B(x;\\,a,b) = \\int_0^x t^{a-1}\\,(1-t)^{b-1}\\,dt\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"255\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> X \u304c\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u5909\u6570\u306e\u5834\u5408\u30011-X \u306f\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u5909\u6570\u3067\u3042\u308a\u3001\u305d\u306e\u30a2\u30eb\u30d5\u30a1 \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3068\u30d9\u30fc\u30bf \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306f\u305d\u308c\u305e\u308c\u5143\u306e\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u30d9\u30fc\u30bf \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3068\u30a2\u30eb\u30d5\u30a1 \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c65dd399bb92ffe982784a6c1b6e5b0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim B(\\alpha,\\beta) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ 1-X\\sim B(\\beta,\\alpha)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"361\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u30a2\u30eb\u30d5\u30a1 \u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u30d9\u30fc\u30bf \u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u4e21\u65b9\u3068\u3082 1 \u306b\u7b49\u3057\u3044\u5834\u5408\u3001\u305d\u306e\u5206\u5e03\u306f\u30d1\u30e9\u30e1\u30fc\u30bf 0 \u3068 1 \u306e\u4e00\u69d8\u5206\u5e03\u3068\u7b49\u4fa1\u3067\u3059\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-10010ad6c6959b44a8ae0fe4361b4034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim B(1,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim U(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"321\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u30d9\u30fc\u30bf\u7248\u914d\u5e03\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u7528\u9014\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u30d9\u30fc\u30bf\u5206\u5e03\u30b0\u30e9\u30d5\u3068\u3053\u306e\u30bf\u30a4\u30d7\u306e\u78ba\u7387\u5206\u5e03\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3092\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002 \u30d9\u30fc\u30bf\u7248\u306e\u914d\u5e03\u3068\u306f\u4f55\u3067\u3059\u304b? 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