{"id":222,"date":"2023-08-03T23:58:33","date_gmt":"2023-08-03T23:58:33","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e3%82%ab%e3%82%99%e3%83%b3%e3%83%9e%e5%88%86%e5%b8%83\/"},"modified":"2023-08-03T23:58:33","modified_gmt":"2023-08-03T23:58:33","slug":"%e3%82%ab%e3%82%99%e3%83%b3%e3%83%9e%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e3%82%ab%e3%82%99%e3%83%b3%e3%83%9e%e5%88%86%e5%b8%83\/","title":{"rendered":"\u30ac\u30f3\u30de\u5206\u5e03"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u30ac\u30f3\u30de\u5206\u5e03\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u7528\u9014\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30ac\u30f3\u30de\u5206\u5e03\u306e\u5b9a\u7fa9\u3001\u305d\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3001\u304a\u3088\u3073\u305d\u306e\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u8868\u73fe\u304c\u3069\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3042\u308b\u304b\u304c\u308f\u304b\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-gamma\"><\/span>\u30ac\u30f3\u30de\u5206\u5e03\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u30ac\u30f3\u30de\u5206\u5e03\u306f\u3001<\/strong> 2 \u3064\u306e\u7279\u6027\u30d1\u30e9\u30e1\u30fc\u30bf \u03b1 \u3068 \u03bb \u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u9023\u7d9a\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u30ac\u30f3\u30de\u5206\u5e03\u306f 2 \u3064\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u5024\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u03b1 \u306f\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf\u3001\u03bb \u306f\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3059\u3002<\/p>\n<p>\u30ac\u30f3\u30de\u5206\u5e03\u306e\u8a18\u53f7\u306f\u30ae\u30ea\u30b7\u30e3\u6587\u5b57\u306e\u5927\u6587\u5b57 \u0393 \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u78ba\u7387\u5909\u6570\u304c\u30ac\u30f3\u30de\u5206\u5e03\u306b\u5f93\u3046\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u8a18\u8ff0\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-1b0ab2e724ffd74455d0907b39f4a598_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\Gamma(\\alpha,\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u30ac\u30f3\u30de\u5206\u5e03\u306f\u3001\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc k = \u03b1 \u3068\u9006\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc \u03b8 = 1\/\u03bb \u3092\u4f7f\u7528\u3057\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u5316\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u5834\u5408\u306b\u304a\u3044\u3066\u3001\u30ac\u30f3\u30de\u5206\u5e03\u3092\u5b9a\u7fa9\u3059\u308b 2 \u3064\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306f\u6b63\u306e\u5b9f\u6570\u3067\u3059\u3002<\/p>\n<p>\u901a\u5e38\u3001\u30ac\u30f3\u30de\u5206\u5e03\u306f\u53f3\u306b\u6b6a\u3093\u3060\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u305f\u3081\u3001\u30b0\u30e9\u30d5\u306e\u5de6\u5074\u306b\u30c7\u30fc\u30bf\u304c\u96c6\u4e2d\u3057\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u30ac\u30f3\u30de\u5206\u5e03\u306f\u96fb\u6c17\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306e\u4fe1\u983c\u6027\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-gamma\"><\/span>\u30ac\u30f3\u30de\u5206\u5e03\u56f3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30ac\u30f3\u30de\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u306f\u3001\u305d\u306e\u7279\u6027\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u5024\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306b\u3001\u30ac\u30f3\u30de\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u304c\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3068\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\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\/trace-de-distribution-gamma.png\" alt=\"\u30ac\u30f3\u30de\u5206\u5e03\u56f3\" class=\"wp-image-4536\" width=\"648\" height=\"388\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4e00\u65b9\u3001\u30ac\u30f3\u30de\u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u4ee5\u4e0b\u306b\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-gamma-probabilite-cumulative.png\" alt=\"\u30ac\u30f3\u30e0\u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\u95a2\u6570\u306e\u30b0\u30e9\u30d5\" class=\"wp-image-4537\" width=\"648\" height=\"388\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-gamma\"><\/span>\u30ac\u30f3\u30de\u5206\u5e03\u306e\u7279\u5fb4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306b\u3001\u30ac\u30f3\u30de\u5206\u5e03\u306e\u7279\u5fb4\u304c\u3069\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3042\u308b\u304b\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u30ac\u30f3\u30de\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u306f\u3001\u305d\u306e 2 \u3064\u306e\u7279\u6027\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306b\u3088\u3063\u3066\u5b8c\u5168\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u03b1 \u306f\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3001\u03bb \u306f\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\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-9640d41832cbcef7d0a7791c55ace57e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha , \\lambda >0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;16&#8243; width=&#8221;62&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u30ac\u30f3\u30de\u5206\u5e03\u306e\u9818\u57df\u306f\u6b63\u306e\u6570\u306e\u307f\u3067\u69cb\u6210\u3055\u308c\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-f543506f97e1f9c5a56ccc4566a3febf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (0,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30ac\u30f3\u30de\u5206\u5e03\u306e\u5e73\u5747\u306f\u3001\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6bd4\u3001\u3064\u307e\u308a \u03b1\/\u03bb \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-326373413d0fe34ef96959dabe9c5cbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{\\alpha}{\\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"78\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30ac\u30f3\u30de\u5206\u5e03\u306e\u5206\u6563\u306f\u3001\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3092\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e 2 \u4e57\u3067\u5272\u3063\u305f\u3082\u306e\u306b\u76f8\u5f53\u3057\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-693a549de92268ac21add32944199974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{\\alpha}{\\lambda^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"107\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> \u03b1 \u306e\u5024\u304c 1 \u672a\u6e80\u306e\u5834\u5408\u3001\u6700\u983b\u5024\u306f 0 \u3067\u3059\u3002\u305f\u3060\u3057\u3001\u03b1 \u304c 1 \u4ee5\u4e0a\u306e\u5834\u5408\u3001\u30ac\u30f3\u30de\u5206\u5e03\u306e\u6700\u983b\u5024\u306f\u6b21\u306e\u5f0f\u3067\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-c9e2762af62f9c38870902ec0284ee07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Mo=0 \\qquad \\text{para } \\alpha<1\\\\[2ex]Mo=\\cfrac{\\alpha-1}{\\lambda} \\qquad \\text{para } \\alpha\\geq1\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"75\" width=\"214\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30ac\u30f3\u30de\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u306e\u5f0f\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-41689ffee11808eab10064a7f3a77693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{\\lambda(\\lambda x)^{\\alpha-1}e^{-\\lambda x}}{\\Gamma(\\alpha)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"168\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001\u0393 \u306f\u30ac\u30f3\u30de\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-6e244faebd1174cb6a56e4254bdaaec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\Gamma(\\alpha)=\\int_0^\\infty t^{\\alpha-1}e^{-t}dt\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"169\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30ac\u30f3\u30de\u5206\u5e03\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u78ba\u7387\u5909\u6570\u306e\u7d2f\u7a4d\u5206\u5e03\u306e\u5f0f\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-6bc3247a247daec5048c409319dc3943_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle F(x)=\\int_0^x\\frac{\\lambda(\\lambda y)^{\\alpha-1}e^{-\\lambda y}}{\\Gamma(\\alpha)}\\;dy\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"224\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf \u03b1 \u304c 1 \u306b\u7b49\u3057\u3044\u5834\u5408\u3001\u30ac\u30f3\u30de\u5206\u5e03\u306f\u540c\u3058\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf \u03bb \u3092\u6301\u3064\u6307\u6570\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-60ed376f92f0db2c22e19f85bb76f828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\Gamma(1,\\lambda) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim \\text{Exp}(\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"321\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc \u03bb \u304c\u5e73\u5747\u306e\u5834\u5408\u3001\u30ac\u30f3\u30de\u5206\u5e03\u306f<a href=\"https:\/\/statorials.org\/ja\/\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\/\">\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03<\/a>\u306e\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\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-efb733464c432d7d1b22ed7e5c534979_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X\\sim \\Gamma\\left(\\frac{n}{2},\\frac{1}{2}\\right) \\text{con } n\\in \\mathbb{N}\\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim \\chi_n^2\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"389\" style=\"vertical-align: 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