{"id":228,"date":"2023-08-03T21:54:17","date_gmt":"2023-08-03T21:54:17","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e3%83%8f%e3%82%9a%e3%83%ac%e3%83%bc%e3%83%88%e3%81%ae%e6%b3%95%e5%89%87\/"},"modified":"2023-08-03T21:54:17","modified_gmt":"2023-08-03T21:54:17","slug":"%e3%83%8f%e3%82%9a%e3%83%ac%e3%83%bc%e3%83%88%e3%81%ae%e6%b3%95%e5%89%87","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e3%83%8f%e3%82%9a%e3%83%ac%e3%83%bc%e3%83%88%e3%81%ae%e6%b3%95%e5%89%87\/","title":{"rendered":"\u30d1\u30ec\u30fc\u30c8\u5206\u5e03"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7d71\u8a08\u306b\u304a\u3051\u308b\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u4f55\u306b\u4f7f\u7528\u3055\u308c\u308b\u306e\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u30b0\u30e9\u30d5\u3068\u3053\u306e\u30bf\u30a4\u30d7\u306e\u78ba\u7387\u5206\u5e03\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3082\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-de-pareto\"><\/span>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306f\u3001<\/strong>\u30d1\u30ec\u30fc\u30c8\u306e\u6cd5\u5247\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u305f\u3081\u306b\u7d71\u8a08\u3067\u4f7f\u7528\u3055\u308c\u308b\u9023\u7d9a\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306f\u3001\u51fa\u73fe\u78ba\u7387\u304c\u6b8b\u308a\u306e\u5024\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u9ad8\u3044\u3044\u304f\u3064\u304b\u306e\u5024\u3092\u6301\u3064\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002<\/p>\n<p>\u30d1\u30ec\u30fc\u30c8\u306e\u6cd5\u5247\u306f 80-20 \u306e\u6cd5\u5247\u3068\u3082\u547c\u3070\u308c\u3001\u73fe\u8c61\u306e\u539f\u56e0\u306e\u307b\u3068\u3093\u3069\u306f\u4eba\u53e3\u306e\u3054\u304f\u4e00\u90e8\u306b\u3088\u308b\u3082\u306e\u3067\u3042\u308b\u3068\u3044\u3046\u7d71\u8a08\u539f\u5247\u3067\u3042\u308b\u3053\u3068\u3092\u601d\u3044\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306b\u306f\u3001\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc x <sub>m<\/sub>\u3068\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc \u03b1 \u3068\u3044\u3046 2 \u3064\u306e\u7279\u5fb4\u7684\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u304c\u3042\u308a\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-c13a66a388e0a7e26781a0e8d9645f40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Pareto}(\\alpha,x_m)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5143\u3005\u3001\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306f\u4eba\u53e3\u5185\u306e\u5bcc\u306e\u5206\u5e03\u3092\u8868\u3059\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u3002\u306a\u305c\u306a\u3089\u3001\u305d\u306e\u5927\u90e8\u5206\u306f\u4eba\u53e3\u306e\u5c11\u6570\u306e\u5272\u5408\u306b\u3088\u308b\u3082\u306e\u3060\u3063\u305f\u304b\u3089\u3067\u3059\u3002\u3057\u304b\u3057\u73fe\u5728\u3001\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306f\u3001\u54c1\u8cea\u7ba1\u7406\u3001\u7d4c\u6e08\u5b66\u3001\u79d1\u5b66\u3001\u793e\u4f1a\u5206\u91ce\u306a\u3069\u3001\u591a\u304f\u306e\u7528\u9014\u306b\u5fdc\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306f\u3001\u5206\u5e03\u3092\u4f5c\u6210\u3057\u305f\u7d4c\u6e08\u5b66\u8005\u306e\u30f4\u30a3\u30eb\u30d5\u30ec\u30c9 \u30d1\u30ec\u30fc\u30c8\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u5f7c\u306f\u30d1\u30ec\u30fc\u30c8\u56f3\u3067\u6700\u3082\u3088\u304f\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002 <\/p>\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\/\u30cf\u309a\u30ec\u30fc\u30c8\u56f3\/\">\u30d1\u30ec\u30fc\u30c8\u56f3\u3068\u306f\u4f55\u3067\u3059\u304b?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-de-pareto\"><\/span>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u8868<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u5b9a\u7fa9\u3092\u7406\u89e3\u3057\u305f\u3068\u3053\u308d\u3067\u3001\u30b0\u30e9\u30d5\u3067\u8868\u3055\u308c\u305f\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u4f8b\u3092\u3044\u304f\u3064\u304b\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u4ee5\u4e0b\u3067\u306f\u3001\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u304c\u7279\u6027\u5024\u306b\u5fdc\u3058\u3066\u3069\u306e\u3088\u3046\u306b\u898b\u3048\u308b\u304b\u3092\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/graphique-de-distribution-de-pareto.png\" alt=\"\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u56f3\" class=\"wp-image-4774\" width=\"587\" height=\"413\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u9818\u57df\u306f\u5024 x <sub>m<\/sub>\u304b\u3089 +\u221e \u307e\u3067\u5909\u5316\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u304c\u3001\u5bc6\u5ea6\u95a2\u6570\u304c x <sub>m<\/sub>\u306e\u5024\u3088\u308a\u524d\u306b\u5b58\u5728\u3057\u306a\u3044\u7406\u7531\u3067\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3001\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\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-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-de-probabilite-pareto-cumulative.png\" alt=\"\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\" class=\"wp-image-4775\" width=\"589\" height=\"414\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-de-pareto\"><\/span>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u7279\u5fb4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4ee5\u4e0b\u306f\u3001\u78ba\u7387\u7406\u8ad6\u3068\u7d71\u8a08\u306b\u95a2\u9023\u3059\u308b\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u6700\u3082\u91cd\u8981\u306a\u7279\u5fb4\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306b\u306f\u3001\u305d\u306e\u66f2\u7dda\u3092\u5b9a\u7fa9\u3059\u308b 2 \u3064\u306e\u7279\u5fb4\u7684\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3001\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc x <sub>m<\/sub>\u3068\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc \u03b1 \u304c\u3042\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-c13a66a388e0a7e26781a0e8d9645f40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Pareto}(\\alpha,x_m)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u9818\u57df\u306f\u3001\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u304b\u3089\u30d7\u30e9\u30b9\u7121\u9650\u5927\u307e\u3067\u306e\u3059\u3079\u3066\u306e\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-c720ee182b49a794ed2862dd83a10ca9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in [x_m,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u03b1 \u304c 1 \u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u5e73\u5747\u306f\u3001\u03b1 \u639b\u3051\u308b x <sub>m<\/sub>\u3068 \u03b1 \u304b\u3089 1 \u3092\u5f15\u3044\u305f\u7a4d\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-6d26513868f9ed6fa45ab0fde0030884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{\\alpha\\cdot x_m}{\\alpha-1}\\quad\\text{para } \\alpha>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;34&#8243; width=&#8221;214&#8243; style=&#8221;vertical-align: -12px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u5206\u6563\u306f\u3001\u5206\u5e03\u306e 2 \u3064\u306e\u7279\u6027\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u4f9d\u5b58\u3057\u3001\u6b21\u306e\u5f0f\u3067\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-6120976b3586b76661d13bb9fdd5375d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Var(X)=\\frac{x_\\mathrm{m}^2\\cdot \\alpha}{(\\alpha-1)^2\\cdot(\\alpha-2)}\\quad \\text{para }\\alpha>2&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;44&#8243; width=&#8221;323&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u4e2d\u592e\u5024\u306f\u3001\u6b21\u306e\u5f0f\u3067\u6c7a\u5b9a\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-0dc2c772a0a0662ad05f8b22c3cf1ba1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Me=x_\\mathrm{m}\\cdot \\sqrt[\\alpha]{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"113\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u6700\u983b\u5024\u306f\u3001\u5206\u5e03\u306e\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc x <sub>m<\/sub>\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-494f2f6e64851f90c504c989d93e22dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=x_m\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30d1\u30ec\u30fc\u30c8\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-1e182771cfe3bf9a145a2ee59b9c7eeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{\\alpha\\cdot x_m^\\alpha}{x^{\\alpha+1}}\\quad\\text{para }x\\geq x_m\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"262\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u540c\u69d8\u306b\u3001\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u7d2f\u7a4d\u78ba\u7387\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-480adc7841b7c72cb4bfecb446ed3fab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=1-\\left(\\frac{x_\\mathrm{m}}{x}\\right)^\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u975e\u5bfe\u79f0\u4fc2\u6570\u306f\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc \u03b1 \u306e\u307f\u306b\u4f9d\u5b58\u3057\u3001\u305d\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-98e7ba5f5d32988033c0f33d6af1bef8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\frac{2(1+\\alpha)}{\\alpha-3}\\,\\sqrt{\\frac{\\alpha-2}{\\alpha}}\\quad\\text{para }\\alpha>3&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;43&#8243; width=&#8221;274&#8243; style=&#8221;vertical-align: -14px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306e\u5c16\u5ea6\u4fc2\u6570\u3082\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc \u03b1 \u306e\u5024\u306b\u5fdc\u3058\u3066\u5909\u5316\u3057\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-989019815fbeb266226cff9aa6b4a52b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\frac{6(\\alpha^3+\\alpha^2-6\\alpha-2)}{\\alpha(\\alpha-3)(\\alpha-4)}\\quad\\text{para }\\alpha>4&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;44&#8243; width=&#8221;299&#8243; style=&#8221;vertical-align: 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