{"id":215,"date":"2023-08-04T01:54:33","date_gmt":"2023-08-04T01:54:33","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e3%82%ab%e3%82%a4%e4%ba%8c%e4%b9%97%e5%88%86%e5%b8%83\/"},"modified":"2023-08-04T01:54:33","modified_gmt":"2023-08-04T01:54:33","slug":"%e3%82%ab%e3%82%a4%e4%ba%8c%e4%b9%97%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e3%82%ab%e3%82%a4%e4%ba%8c%e4%b9%97%e5%88%86%e5%b8%83\/","title":{"rendered":"\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u30ab\u30a4\u4e8c\u4e57\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\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u30b0\u30e9\u30d5\u3068\u305d\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3082\u8868\u793a\u3055\u308c\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-chi-cuadrado\"><\/span>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306f\u3001<\/strong>\u8a18\u53f7\u304c \u03c7\u00b2 \u3067\u3042\u308b\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u3088\u308a\u6b63\u78ba\u306b\u306f\u3001\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306f\u3001\u6b63\u898f\u5206\u5e03\u3092\u6301\u3064<em>k \u500b<\/em>\u306e\u72ec\u7acb\u78ba\u7387\u5909\u6570\u306e\u4e8c\u4e57\u306e\u5408\u8a08\u3067\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306b\u306f<em>k \u500b<\/em>\u306e\u81ea\u7531\u5ea6\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306f\u3001\u305d\u308c\u304c\u8868\u3059\u6b63\u898f\u5206\u5e03\u5909\u6570\u306e\u4e8c\u4e57\u548c\u3068\u540c\u3058\u304f\u3089\u3044\u306e\u81ea\u7531\u5ea6\u3092\u6301\u3061\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-9ea0bf7a87071883ceae5e419bae9e71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X\\sim\\chi^2_k \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\begin{array}{l}\\text{Distribuci\\'on chi-cuadrado}\\\\[2ex]\\text{con k grados de libertad}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"404\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306f\u3001<strong>\u30d4\u30a2\u30bd\u30f3\u5206\u5e03<\/strong>\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306f\u30ac\u30f3\u30de\u5206\u5e03\u306e\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306f\u3001\u4eee\u8aac\u691c\u5b9a\u3084\u4fe1\u983c\u533a\u9593\u306a\u3069\u306e\u7d71\u8a08\u7684\u63a8\u8ad6\u3067\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u30bf\u30a4\u30d7\u306e\u78ba\u7387\u5206\u5e03\u304c\u3069\u306e\u3088\u3046\u306b\u5fdc\u7528\u3055\u308c\u308b\u304b\u3092\u4ee5\u4e0b\u3067\u898b\u3066\u3044\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-chi-cuadrado\"><\/span>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u30b0\u30e9\u30d5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u5b9a\u7fa9\u3092\u7406\u89e3\u3059\u308b\u3068\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u5206\u5e03\u306e\u4f8b\u304c\u3044\u304f\u3064\u304b\u30b0\u30e9\u30d5\u3067\u8868\u3055\u308c\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u3067\u306f\u3001\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u78ba\u7387\u30d7\u30ed\u30c3\u30c8\u304c\u81ea\u7531\u5ea6\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\/diagramme-de-distribution-du-chi-carre.png\" alt=\"\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u30d7\u30ed\u30c3\u30c8\" class=\"wp-image-4212\" width=\"670\" height=\"405\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u306f\u4e0a\u306e\u30b0\u30e9\u30d5\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u4e00\u65b9\u3001\u30ab\u30a4\u4e8c\u4e57\u7d2f\u7a4d\u78ba\u7387\u5206\u5e03\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\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-du-chi-carre-cumulatif.png\" alt=\"\u30ab\u30a4\u4e8c\u4e57\u7d2f\u7a4d\u5206\u5e03\u30b0\u30e9\u30d5\" class=\"wp-image-4215\" width=\"670\" height=\"405\" 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>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u8868<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-chi-cuadrado\"><\/span>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u7279\u5fb4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u78ba\u7387\u7406\u8ad6\u3068\u7d71\u8a08\u306b\u95a2\u9023\u3059\u308b\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u6700\u3082\u91cd\u8981\u306a\u7279\u6027\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u5e73\u5747\u306f\u3001\u305d\u306e\u81ea\u7531\u5ea6\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-8a7926aa60ec788064c47a5a34e641ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim\\chi^2_k\\\\[2ex] E[X]=k\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"73\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u5206\u6563\u306f\u3001\u5206\u5e03\u306e\u81ea\u7531\u5ea6\u306e 2 \u500d\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-cffd659f19d8ed8260fcaf53dc6dd83f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim\\chi^2_k\\\\[2ex] Var(X)=2\\cdot k\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u6700\u983b\u5024\u306f\u3001\u5206\u5e03\u306b\u8907\u6570\u306e\u81ea\u7531\u5ea6\u304c\u3042\u308b\u9650\u308a\u3001\u305d\u306e\u81ea\u7531\u5ea6\u3088\u308a 2 \u5358\u4f4d\u5c0f\u3055\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-3c10387635aba8249e98afe0ca6f3ea9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=k-2 \\qquad \\text{si } k\\geq 2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"186\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> x=0 \u306e\u5834\u5408\u3001\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u306f\u30bc\u30ed\u3067\u3059\u3002\u305f\u3060\u3057\u3001x \u306e\u5024\u304c 0 \u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u306f\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-f239003e822b2c8ba44146e94a94ad89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]= \\frac{(1\/2)^{k\/2}}{\\Gamma(k\/2)} x^{k\/2 - 1} e^{-x\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"254\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306f\u3001\u6b21\u306e\u5f0f\u306b\u3088\u3063\u3066\u6c7a\u307e\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-9d39bc2eb949e628c1109501656da4b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{\\gamma(k\/2,x\/2)}{\\Gamma(k\/2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"187\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u6b6a\u5ea6\u4fc2\u6570\u306f\u30018 \u3092\u5206\u5e03\u306e\u81ea\u7531\u5ea6\u306e\u6570\u3067\u5272\u3063\u305f\u5546\u306e\u5e73\u65b9\u6839\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-c0113d9ec77836abace7fe06e18d90c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\sqrt{\\frac{8}{k}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"69\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u5c16\u5ea6\u306f\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\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-a2c6ae2842ea42a7ff31babce8eb778a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C=3+\\cfrac{12}{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"88\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u306b\u3088\u308a\u3001 <em>k<\/em>\u304c\u5341\u5206\u306b\u5927\u304d\u3044\u5834\u5408\u3001\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306f\u6b63\u898f\u5206\u5e03\u3067\u8fd1\u4f3c\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-b2c7e4c59f39b5f1910f7a7806c08819_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{k \\to \\infty} \\frac{\\chi^2_k (x)}{ k } = N_{\\left(1,\\sqrt{2\/k}\\right)} (x)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"210\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-distribucion-chi-cuadrado\"><\/span>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u5fdc\u7528<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306f\u3001\u7d71\u8a08\u5b66\u306b\u304a\u3044\u3066\u3055\u307e\u3056\u307e\u306a\u7528\u9014\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u5b9f\u969b\u3001\u5909\u6570\u9593\u306e\u72ec\u7acb\u6027\u3068\u7406\u8ad6\u7684\u5206\u5e03\u3078\u306e\u9069\u5408\u5ea6\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u30ab\u30a4\u4e8c\u4e57\u691c\u5b9a\u3055\u3048\u3042\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u30ab\u30a4\u4e8c\u4e57\u691c\u5b9a\u3092\u4f7f\u7528\u3057\u3066\u3001\u30b5\u30f3\u30d7\u30eb\u306e\u30c7\u30fc\u30bf\u304c\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306b\u6e96\u62e0\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u7dda\u5f62\u56de\u5e30\u5206\u6790\u3067\u306f\u3001\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306f\u3001\u6b63\u898f\u5206\u5e03\u3057\u305f\u6bcd\u96c6\u56e3\u306e\u5e73\u5747\u3092\u63a8\u5b9a\u3057\u3001\u7dda\u5f62\u56de\u5e30\u5206\u6790\u306e\u76f4\u7dda\u306e\u50be\u304d\u3092\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u3082\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u6700\u5f8c\u306b\u3001\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u3082\u3001Snedecor F \u5206\u5e03\u3068\u306e\u95a2\u4fc2\u3092\u901a\u3058\u3066\u5206\u6563\u5206\u6790\u306b\u53c2\u52a0\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u30ab\u30a4\u4e8c\u4e57\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\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u30b0\u30e9\u30d5\u3068\u305d\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3082\u8868\u793a\u3055\u308c\u307e\u3059\u3002 \u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u3068\u306f\u4f55\u3067\u3059\u304b? \u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306f\u3001\u8a18\u53f7\u304c \u03c7\u00b2 \u3067\u3042\u308b\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u3088\u308a\u6b63\u78ba\u306b\u306f\u3001 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