{"id":217,"date":"2023-08-04T01:16:05","date_gmt":"2023-08-04T01:16:05","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e5%ad%a6%e7%94%9f%e3%81%ae%e5%88%86%e5%b8%83\/"},"modified":"2023-08-04T01:16:05","modified_gmt":"2023-08-04T01:16:05","slug":"%e5%ad%a6%e7%94%9f%e3%81%ae%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e5%ad%a6%e7%94%9f%e3%81%ae%e5%88%86%e5%b8%83\/","title":{"rendered":"\u5b66\u751f\u306e t \u5206\u5e03"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001Student t \u5206\u5e03\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u7528\u9014\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u30b0\u30e9\u30d5\u3068\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u78ba\u7387\u5206\u5e03\u306e\u7279\u5fb4\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-t-de-student\"><\/span>\u5b66\u751f\u306e\u5206\u5e03\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306f\u3001<\/strong>\u7d71\u8a08\u3067\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u3044\u308b\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306f\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u691c\u5b9a\u3067\u4f7f\u7528\u3055\u308c\u30012 \u3064\u306e\u30b5\u30f3\u30d7\u30eb\u306e\u5e73\u5747\u9593\u306e\u5dee\u3092\u6c7a\u5b9a\u3057\u3001\u4fe1\u983c\u533a\u9593\u3092\u78ba\u7acb\u3057\u307e\u3059\u3002<\/p>\n<p>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306f\u3001\u7d71\u8a08\u5b66\u8005\u30a6\u30a3\u30ea\u30a2\u30e0 \u30b7\u30fc\u30ea\u30fc \u30b4\u30bb\u30c3\u30c8\u306b\u3088\u3063\u3066 1908 \u5e74\u306b\u300c\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u300d\u3068\u3044\u3046\u4eee\u540d\u3067\u958b\u767a\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n<p>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306f\u3001\u89b3\u6e2c\u5024\u306e\u7dcf\u6570\u304b\u3089 1 \u5358\u4f4d\u3092\u6e1b\u7b97\u3059\u308b\u3053\u3068\u3067\u5f97\u3089\u308c\u308b\u81ea\u7531\u5ea6\u306e\u6570\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u81ea\u7531\u5ea6\u3092\u6c7a\u5b9a\u3059\u308b\u5f0f\u306f<em>\u03bd=n-1<\/em>\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-1c805dc2d6ca050feb70dad99de53402_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\nu=n-1\\\\[2ex]X\\sim t_\\nu\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"74\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-t-de-student\"><\/span>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u30b0\u30e9\u30d5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u5b9a\u7fa9\u304c\u308f\u304b\u3063\u305f\u306e\u3067\u3001\u305d\u306e\u30b0\u30e9\u30d5\u304c\u3069\u306e\u3088\u3046\u306a\u3082\u306e\u304b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u4ee5\u4e0b\u3067\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u81ea\u7531\u5ea6\u3092\u6301\u3064\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u30b0\u30e9\u30d5\u3067\u898b\u308b\u3053\u3068\u304c\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\/graphique-de-distribution-t-des-etudiants.png\" alt=\"\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u30b0\u30e9\u30d5\" class=\"wp-image-4266\" width=\"700\" height=\"420\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u30b0\u30e9\u30d5\u304b\u3089\u3001\u6b21\u306e\u7279\u6027\u3092\u63a8\u5b9a\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:14px\"><span style=\"color:#101010;font-weight: normal;\">\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8 t \u5206\u5e03\u306f 0 \u3092\u4e2d\u5fc3\u3068\u3057\u3066\u5bfe\u79f0\u3067\u3042\u308a\u3001\u91e3\u9418\u578b\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:14px\"><span style=\"color:#101010;font-weight: normal;\">\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306f\u6b63\u898f\u5206\u5e03\u3088\u308a\u3082\u5206\u6563\u3057\u3066\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u66f2\u7dda\u306f\u5e45\u304c\u5e83\u304f\u306a\u308a\u307e\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:14px\"><span style=\"color:#101010;font-weight: normal;\">\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u81ea\u7531\u5ea6\u304c\u5927\u304d\u304f\u306a\u308b\u307b\u3069\u3001\u305d\u306e\u5206\u6563\u306f\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002<\/span><\/li>\n<\/ul>\n<p>\u4e0a\u306e\u30b0\u30e9\u30d5\u3067\u306f\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u304c\u81ea\u7531\u5ea6\u306b\u5bfe\u3057\u3066\u30d7\u30ed\u30c3\u30c8\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\u95a2\u6570\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u4ee5\u4e0b\u3067\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-t-etudiante-cumulative.png\" alt=\"\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e\u7d2f\u7a4d t \u5206\u5e03\u306e\u30d7\u30ed\u30c3\u30c8\" class=\"wp-image-4267\" width=\"700\" height=\"420\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong><a href=\"https:\/\/statorials.org\/ja\/\u5b66\u751f-t-\u5206\u5e03\u8868\/\">\u751f\u5f92\u306e\u5206\u5e03\u8868<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-t-de-student\"><\/span>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u7279\u5fb4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u6700\u3082\u91cd\u8981\u306a\u7279\u5fb4\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li> Student t \u5206\u5e03\u306e\u9818\u57df\u306f\u5b9f\u6570\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-fd8ca9914bdf447012a1a16f7950ce95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (-\\infty, +\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u8907\u6570\u306e\u81ea\u7531\u5ea6\u3092\u6301\u3064\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u5834\u5408\u3001\u5206\u5e03\u306e\u5e73\u5747\u306f 0 \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-d4fed5eadcaa1162752aeedb7f8a0906_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim t_\\nu\\\\[2ex] E[X]=0 \\qquad \\text{para }\\nu>1\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;55&#8243; width=&#8221;190&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \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-bfdcbc8a5f071a61e091b0ef6f686a16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim t_\\nu\\\\[2ex] Var(X)=\\cfrac{\\nu}{\\nu-2} \\qquad \\text{para }\\nu>2\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;75&#8243; width=&#8221;245&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u4e2d\u592e\u5024\u3068\u6700\u983b\u5024\u306f\u3001\u81ea\u7531\u5ea6\u306e\u6570\u306b\u95a2\u4fc2\u306a\u304f\u3001\u5e38\u306b 0 \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-8d90790fce0c987648c0b30216c82214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Me=0\\\\[2ex]Mo=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"60\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8 t \u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u306f\u3001\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\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-8c0f1e97a8e407e8b9e2b00ba93aee0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{\\Gamma((\\nu+1)\/2)} {\\sqrt{\\nu\\pi}\\,\\Gamma(\\nu\/2)} (1+x^2\/\\nu)^{-(\\nu+1)\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"339\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\u5206\u5e03\u95a2\u6570\u306f\u3001\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\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-da1e3bdf2d87c3a7dcc89c236958dcec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{1}{2} + x \\Gamma \\left( \\frac{\\nu+1}{2} \\right) \\cdot\\frac{\\,_2F_1 \\left ( \\frac{1}{2},\\frac{\\nu+1}{2};\\frac{3}{2};-\\frac{x^2}{\\nu} \\right)}{\\sqrt{\\pi\\nu}\\,\\Gamma \\left(\\frac{\\nu}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"402\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<ul>\n<li>\u81ea\u7531\u5ea6\u304c 3 \u3088\u308a\u5927\u304d\u3044\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8 t \u5206\u5e03\u306e\u5834\u5408\u3001\u5bfe\u79f0\u5206\u5e03\u3067\u3042\u308b\u305f\u3081\u3001\u975e\u5bfe\u79f0\u4fc2\u6570\u306f 0 \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-6fea0ec5e37ef4db61fb44d6f5eba6fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=0\\qquad \\text{para }\\nu>3&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;17&#8243; width=&#8221;164&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u81ea\u7531\u5ea6\u304c 4 \u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u5c16\u5ea6\u306f\u30016 \u3092\u81ea\u7531\u5ea6\u304b\u3089 4 \u3092\u5f15\u3044\u305f\u5024\u3067\u5272\u308b\u3053\u3068\u306b\u3088\u3063\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-0335e705ad289732dd1be59dc8388dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\cfrac{6}{\\nu-4}\\qquad \\text{para }\\nu>4&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;38&#8243; width=&#8221;198&#8243; style=&#8221;vertical-align: -12px;&#8221;><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-distribucion-t-de-student\"><\/span>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t \u5206\u5e03\u306e\u5fdc\u7528<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e t 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