{"id":2107,"date":"2020-07-24T11:00:00","date_gmt":"2020-07-24T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=2107"},"modified":"2020-08-11T11:15:18","modified_gmt":"2020-08-11T02:15:18","slug":"dpoid-mv","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/dpoid-mv","title":{"rendered":"\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011"},"content":{"rendered":"\n

\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2605\u2606\u2606\u2606<\/span><\/p>\n\n\n\n\n\n\n\n

\u3053\u306e\u8a18\u4e8b\u3067\u306f\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u3092\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9\u304c\u5206\u304b\u3089\u306a\u3044\u65b9\u306f\u662f\u975e\u304a\u8aad\u307f\u304f\u3060\u3055\u3044\u3002\u305d\u306e\u4ed6\u306e\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831\u306f\uff1c\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\uff1e<\/a>\u306e\u8a18\u4e8b\u3092\u304a\u8aad\u307f\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n\n

\n \n
\"\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\"<\/div>\n
\n
\u30dd\u30a2\u30bd\u30f3\u5206\u5e03<\/div>\n
\u3000\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\uff08Poisson distribution\uff09\u306f\u96e2\u6563\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306f\u4e00\u5b9a\u9593\u9694\u306e\u6642\u9593\u3067\u767a\u751f\u3059\u308b\u4e8b\u8c61\u306e\u6570\u3092\u8868\u3057\u307e\u3059\u3002\u3082\u3046\u2026<\/div>\n <\/div>\n
<\/div>\n <\/a>\n <\/div>\n\n\n\n

\u3000<\/p>\n\n\n\n

\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563<\/h2>\n\n\n\n
\u671f\u5f85\u5024\u3068\u5206\u6563<\/strong><\/div>\n
\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\lambda\\)\u306e\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\sim Po(\\lambda)\\)\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n
\\begin{align}\n\\mathrm{E}[X]=\\lambda,\\ \\ \\ \\mathrm{Var}[X]=\\lambda\n\\end{align}<\/div>\n<\/div>\n\n\n\n

\u671f\u5f85\u5024\u30fb\u5206\u6563\u3092\u6c42\u3081\u308b\u969b\u306b\u306f\uff1c\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\uff1e<\/a>\u304a\u3088\u3073\uff1c\u5206\u6563\u306e\u5b9a\u7fa9\uff1e<\/a>\u3092\u4f7f\u7528\u3059\u308b\u306e\u3067\u3001\u899a\u3048\u3066\u3044\u306a\u3044\u65b9\u306f\u8a3c\u660e\u3092\u8aad\u3080\u524d\u306b\u4e00\u5ea6\u3001\u76ee\u3092\u901a\u3057\u3066\u304a\u3044\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\u3000<\/p>\n\n\n\n

\u8a3c\u660e<\/h4>\n\n\n\n

\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\lambda\\)\u306e\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\)\u306e\u78ba\u7387\u95a2\u6570\u306f

\\begin{align}
f(x)= \\frac{\\lambda^{x}e^{-\\lambda}}{x!}
\\end{align}<\/div>
\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u306f<\/a><\/a><\/a><\/a>\uff1c\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831\uff1e<\/a>\u3092\u304a\u8aad\u307f\u304f\u3060\u3055\u3044\u3002
\u3000\u307e\u305a\u3001\u671f\u5f85\u5024\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\u304b\u3089
\\begin{align}
\\mathrm{E}[X] &= \\sum_{x=0}^{\\infty}xf(x) \\\\
&= \\sum_{x=1}^{\\infty}x\\frac{\\lambda^{x}e^{-\\lambda}}{x!} \\\\
&= \\lambda \\sum_{x=1}^{\\infty}\\frac{\\lambda^{x-1}e^{-\\lambda}}{(x-1)!} \\\\
&= \\lambda
\\end{align}<\/div>
\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u6700\u5f8c\u306e\u884c\u306e\u5909\u5f62\u306f\u3001
\\begin{align}
\\sum_{x=1}^{\\infty}\\frac{\\lambda^{x-1}e^{-\\lambda}}{(x-1)!}
\\end{align}<\/div>
\u306b\u3064\u3044\u3066\u898b\u3066\u307f\u308b\u3068\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\lambda,\\ (x-1)\\)\u306e\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306e\u78ba\u7387\u95a2\u6570\u306e\u7dcf\u548c\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u3067\u3001\\(1\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u8003\u3048\u65b9\u306f\u5206\u6563\u3092\u6c42\u3081\u308b\u3068\u304d\u306b\u3082\u7528\u3044\u307e\u3059\u3002
\u3000\uff1c\u5206\u6563\u306e\u5b9a\u7fa9\uff1e<\/a>\u306e\u8a18\u4e8b\u304b\u3089\u5206\u6563\u306f
\\begin{align}
\\mathrm{Var}[X] &= \\mathrm{E}[X^{2}]-\\mathrm{E}[X]^{2}
\\end{align}<\/div>
\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3001\\(\\mathrm{E}[X^{2}]\\)\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3088\u3063\u3066
\\begin{align}
\\mathrm{E}[X^{2}] &= \\sum_{x=0}^{\\infty}x^{2}f(x) \\\\
&= \\sum_{x=1}^{\\infty}\\{x(x-1)+x\\}\\frac{\\lambda^{x}e^{-\\lambda}}{x!} \\\\
&= \\sum_{x=2}^{\\infty}x(x-1)\\frac{\\lambda^{x}e^{-\\lambda}}{x!} + \\sum_{x=1}^{\\infty}x\\frac{\\lambda^{x}e^{-\\lambda}}{x!} \\\\
&= \\lambda^{2}\\sum_{x=2}^{\\infty}\\frac{\\lambda^{x-2}e^{-\\lambda}}{(x-2)!} + \\mathrm{E}[X] \\\\
&= \\lambda^{2}+\\lambda
\\end{align}<\/div>
\u3068\u306a\u308b\u3053\u3068\u304b\u3089\u6c42\u3081\u305f\u3044\u5206\u6563\u3092\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u25a1<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2605\u2606\u2606\u2606 \u3053\u306e\u8a18\u4e8b\u3067\u306f\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u3092\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9\u304c\u5206\u304b\u3089\u306a\u3044 … <\/p>\n","protected":false},"author":1,"featured_media":2094,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[74,72],"tags":[108,31,73],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\uff08\u78ba\u7387\u95a2\u6570\uff09.png","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2107"}],"collection":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/comments?post=2107"}],"version-history":[{"count":6,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2107\/revisions"}],"predecessor-version":[{"id":2206,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2107\/revisions\/2206"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/2094"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=2107"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=2107"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=2107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}