{"id":2064,"date":"2020-07-22T11:00:00","date_gmt":"2020-07-22T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=2064"},"modified":"2020-07-19T20:39:29","modified_gmt":"2020-07-19T11:39:29","slug":"categorical-distribution","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/categorical-distribution","title":{"rendered":"\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\uff08\u30ab\u30c6\u30b4\u30ea\u30ab\u30eb\u5206\u5e03\uff09"},"content":{"rendered":"\n\n\n\n\n<p>\u3000\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\uff08categorical distribution\uff09\uff08\u30ab\u30c6\u30b4\u30ea\u30ab\u30eb\u5206\u5e03\u30fb\u4e00\u822c\u5316\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u30fbmultinoulli\u5206\u5e03\uff09\u306f\u96e2\u6563\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u5206\u5e03\u306e\u65e5\u672c\u8a9e\u540d\u306f\u3042\u307e\u308a\u5b9a\u7740\u3057\u3066\u3044\u306a\u3044\u306e\u3067\u3001\u547c\u3073\u65b9\u306f\u69d8\u3005\u306a\u3082\u306e\u304c\u3042\u308a\u307e\u3059\uff08\u3053\u3046\u3044\u3046\u5834\u5408\u3001\u82f1\u8a9e\u540d\u3092\u305d\u306e\u307e\u307e\u4f7f\u7528\u3059\u308b\u306e\u304c\u666e\u901a\u3067\u3059\uff09\u3002<br>\u3000\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u306f\\(1\\)\u56de\u306e\u8a66\u884c\u3067\\(k\\)\u901a\u308a\u306e\u30d1\u30bf\u30fc\u30f3\\(A_{1},\\cdots,A_{k}\\)\u304c\u5f97\u3089\u308c\u308b\u3068\u304d\u306e\u3001\u78ba\u7387\u5206\u5e03\u3092\u8868\u3057\u307e\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u30d1\u30bf\u30fc\u30f3\u304c\u5f97\u3089\u308c\u308b\u78ba\u7387\u3092<br><div style=\"overflow-x: auto;\">\\begin{align}<br>p_{i}=\\mathrm{P}(A_{i}),\\ \\ \\ i=1,\\cdots,k<br>\\end{align}<\/div><br>\u3068\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u3001\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831\u3068\u4e3b\u306a\u6027\u8cea\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<div id=\"toc_container\" class=\"toc_light_blue no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u3068\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">3<\/span> \u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9<\/a><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">4<\/span> \u7a4d\u7387\u6bcd\u95a2\u6570\u30fb\u7279\u6027\u95a2\u6570\u306e\u6c42\u3081\u65b9<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_1\">5<\/span> \u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u3068\u95a2\u9023\u6df1\u3044\u5206\u5e03<\/a><\/li><\/ul><\/div>\n<h2><span id=\"i\">\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831<\/span><\/h2>\n\n\n\n<p>\u203b\u3000\u8868\u306f\u6a2a\u306b\u30b9\u30af\u30ed\u30fc\u30eb\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\">\n<table style=\"width: 100%; height: 330px;\">\n<tbody>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\">\u30d1\u30e9\u30e1\u30fc\u30bf<\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\(0 &lt; k\\)\uff08\\(k\\)\u306f\u30ab\u30c6\u30b4\u30ea\u6570\u3092\u8868\u3057\u307e\u3059\u3002\uff09<br \/>\\(p_{1},\\cdots,p_{k}\\)\uff08\\(p_{i}\\)\u306f\u4e8b\u8c61\\(A_{i}\\)\u304c\u8d77\u3053\u308b\u78ba\u7387\u3092\u8868\u3057\u307e\u3059\u3002\uff09<\/td>\n<\/tr>\n<tr style=\"height: 56px;\">\n<td style=\"width: 17.5862%; height: 56px;\">\u78ba\u7387\u5909\u6570\u306e\u7bc4\u56f2<\/td>\n<td style=\"width: 82.2414%; height: 56px;\">\\(1\\leq x \\leq k\\)\u3000\u3000\\(x\\)\u306f\u6574\u6570<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/probability-function\">\u78ba\u7387\u95a2\u6570<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\(\\mathrm{P}(A_{i})=p_{i}\\)<br \/>\u3082\u3057\u304f\u306f<br \/>\\(p(x)=[x=1]p_{1}+[x=2]p_{2}+\\cdots+[x=k]p_{k}\\)<br \/><br \/>\u3053\u3053\u3067\\([x=i]\\)\u306f\u30a2\u30a4\u30d0\u30fc\u30bd\u30f3\u30d6\u30e9\u30b1\u30c3\u30c8\u3067\u3042\u308a\u3001\\([\\ast]\\)\u306f\\(\\ast\\)\u304c\u771f\u306e\u3068\u304d\\(1\\)\u3001<br \/>\u507d\u306e\u3068\u304d\\(0\\)\u3092\u8868\u3057\u307e\u3059\uff08\u30af\u30ed\u30cd\u30c3\u30ab\u30fc\u306e\u30c7\u30eb\u30bf\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\uff09\u3002<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mgf\">\u7a4d\u7387\u6bcd\u95a2\u6570<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\(\\displaystyle\\sum_{i=1}^{k}p_{i}\\exp[t_{i}]\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 38px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cf\">\u7279\u6027\u95a2\u6570<\/a><\/td>\n<td style=\"width: 82.2414%; height: 38px;\">\\(\\displaystyle\\sum_{j=1}^{k}p_{j}\\exp[it_{j}]\\)<\/td>\n<\/tr>\n<tr style=\"height: 56px;\">\n<td style=\"width: 17.5862%; height: 56px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cgf\">\u30ad\u30e5\u30e0\u30e9\u30f3\u30c8\u6bcd\u95a2\u6570<\/a><\/td>\n<td style=\"width: 82.2414%; height: 56px;\">\\( \\log p+t-\\log \\{1-(1-p)e^{t}\\} ,\\ \\ \\ t &lt; -\\log (1-p) \\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition\">\u671f\u5f85\u5024<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\( \\displaystyle p_{i} \\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 17.5862%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/variance\">\u5206\u6563<\/a><\/td>\n<td style=\"width: 82.2414%; height: 36px;\">\\(\u00a0 p_{i}(1-p_{i}) \\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n\n\n\n<h2><span id=\"i-2\">\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u3068\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03<\/span><\/h2>\n\n\n\n<p>\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u306b\u304a\u3044\u3066\\(k=2\\)\u3001\\(p_{1}=p\\)\u3001\\(p_{2}=1-p\\)\u3068\u3059\u308c\u3070\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u3068\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306f\u4e00\u81f4\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u3068\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306e\u5b9a\u7fa9\u304b\u3089\u660e\u3089\u304b\u3067\u3059\u3002<\/p>\n\n\n\n<h2><span id=\"i-3\">\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9<\/span><\/h2>\n\n\n\n<div style=\"display: inline-block; background: #33cc33; padding: 5px 10px; color: #ffffff; border-radius: 5px 5px 0 0;\"><strong>\u671f\u5f85\u5024\u3068\u5206\u6563<\/strong><\/div>\n<div style=\"background: #ffffea; padding: 10px; border: 2px solid #33cc33;\">\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\uff08\\(k;p_{1},\\cdots,p_{k}\\)\uff09\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n<div style=\"overflow-x: auto;\">\\begin{align}\n\\mathrm{E}[X_{i}]=p_{i},\\ \\ \\ \\mathrm{Var}[X_{i}]=p_{i}(1-p_{i})\n\\end{align}<\/div>\n<\/div>\n\n\n\n<h3>\u8a3c\u660e<\/h3>\n\n\n\n<p>\u3000\u78ba\u7387\u5909\u6570\\(X_{i}\\)\u306f\\(A_{i}\\)\u304c\u8d77\u3053\u308c\u3070\\(1\\)\u3001\u305d\u308c\u4ee5\u5916\u306a\u3089\\(0\\)\u3068\u306a\u308b\u3082\u306e\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition\">\uff1c\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\uff1e<\/a>\u3088\u308a<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\mathrm{E}[X_{i}] &amp;= \\sum_{\\ell=1}^{k}x_{\\ell}f(x_{\\ell})\\\\<br>&amp;= x_{1}f(x_{1}) + \\cdots + x_{i}f(x_{i}) + \\cdots +x_{k}f(x_{k}) \\\\<br>&amp;= 0\\cdot p_{1} + \\cdots + 1\\cdot p_{i} + \\cdots + 0\\cdot p_{k} \\\\<br>&amp;= p_{i}<br>\\end{align}<\/div><br>\u304c\u6210\u7acb\u3057\u307e\u3059\u3002<br>\u3000\u3042\u3068\u306f\u5206\u6563\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/variance\">\uff1c\u5206\u6563\u306e\u5b9a\u7fa9\uff1e<\/a>\u306e\u8a18\u4e8b\u304b\u3089\u5206\u6563\u306f<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\mathrm{Var}[X] &amp;= \\mathrm{E}[X^{2}]-\\mathrm{E}[X]^{2}<br>\\end{align}<\/div><br>\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\u3053\u308c\u3082\u3001<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition\">\uff1c\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\uff1e<\/a>\u3088\u308a<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\mathrm{E}[X_{i}] &amp;= \\sum_{\\ell=1}^{k}x_{\\ell}^{2}f(x_{\\ell})\\\\<br>&amp;= x_{1}^{2}f(x_{1}) + \\cdots + x_{i}^{2}f(x_{i}) + \\cdots +x_{k}^{2}f(x_{k}) \\\\<br>&amp;= 0\\cdot p_{1} + \\cdots + 1\\cdot p_{i} + \\cdots + 0\\cdot p_{k} \\\\<br>&amp;= p_{i}<br>\\end{align}<\/div><br>\u304c\u6210\u7acb\u3059\u308b\u306e\u3067\u3001\u6c42\u3081\u305f\u3044\u5206\u6563\u306f\u3001<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\mathrm{Var}[X_{i}] = p_{i}-p_{i}^{2} = p_{i}(1-p_{i})<br>\\end{align}<\/div><br>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"has-text-align-right\">\u25a1<\/p>\n\n\n\n<h2><span id=\"i-4\">\u7a4d\u7387\u6bcd\u95a2\u6570\u30fb\u7279\u6027\u95a2\u6570\u306e\u6c42\u3081\u65b9<\/span><\/h2>\n\n\n\n<div style=\"display: inline-block; background: #33cc33; padding: 5px 10px; color: #ffffff; border-radius: 5px 5px 0 0;\"><strong>\u7a4d\u7387\u6bcd\u95a2\u6570\u3068\u7279\u6027\u95a2\u6570<\/strong><\/div>\n<div style=\"background: #ffffea; padding: 10px; border: 2px solid #33cc33;\">\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\uff08\\(k;p_{1},\\cdots,p_{k}\\)\uff09\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u30fb\u7279\u6027\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n<div style=\"overflow-x: auto;\">\\begin{align}\nM_{X}(t)=\\sum_{i=1}^{k}p_{i}\\exp[t_{i}],\\ \\ \\ \\phi_{X}(t)[X_{i}]=\\sum_{j=1}^{k}p_{j}\\exp[it_{j}]\n\\end{align}<\/div>\n<\/div>\n\n\n\n<h3>\u8a3c\u660e<\/h3>\n\n\n\n<p>\u3000\u78ba\u7387\u5909\u6570\\(X= ^{T}(X_{1},\\cdots,X_{k})\\)\u306e\\(k\\)\u5909\u91cf\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308a\u3001\\(X_{i}\\)\u306f\u4e8b\u8c61\\(A_{i}\\)\u304c\u8d77\u3053\u308c\u3070\\(1\\)\u3001\u8d77\u3053\u3089\u306a\u3051\u308c\u3070\\(0\\)\u3092\u8868\u3059\u3082\u306e\u3068\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u5909\u6570\\(t\\)\u306f\\(t= ^{T}(t_{1},\\cdots,t_{k})\\)\u306e\\(k\\)\u6b21\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308a\u3001<br><div style=\"overflow-x: auto;\">\\begin{align}<br>tX = t_{1}X_{1} + \\cdots + t_{k}X_{k} = \\sum_{i=1}^{k}t_{i}X_{i}<br>\\end{align}<\/div><br>\u3092\u8868\u3059\u3082\u306e\u3068\u3057\u307e\u3059\u3002<br>\u3000\u307e\u305a\u3001\u7a4d\u7387\u6bcd\u95a2\u6570\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mgf\">\uff1c\u7a4d\u7387\u6bcd\u95a2\u6570\u306e\u5b9a\u7fa9\uff1e<\/a>\u3068<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition\">\uff1c\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\uff1e<\/a>\u304b\u3089<br><div style=\"overflow-x: auto;\">\\begin{align}<br>M_{X}(t) &amp;= \\mathrm{E}\\left[ \\exp[tX] \\right] \\\\<br>&amp;= \\mathrm{E}\\left[ \\exp\\left[ \\sum_{i=1}^{k}t_{i}X_{i} \\right] \\right] \\\\<br>&amp;= \\sum_{j=1}^{k} \\exp\\left[ \\sum_{i=1}^{k}t_{i}x_{i} \\right]f(x_{j}) \\\\<br>&amp;= \\sum_{j=1}^{k} p_{j}\\exp\\left[ t_{j} \\right]<br>\\end{align}<\/div><br>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u3001<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\sum_{j=1}^{k} \\exp\\left[ \\sum_{i=1}^{k}t_{i}x_{i} \\right]f(x_{j})<br>\\end{align}<\/div><br>\u306b\u3064\u3044\u3066\u898b\u3066\u307f\u307e\u3059\u3002\\(i\\neq j\\)\u3068\u306a\u308b\u3068\u3053\u308d\u3067\u306f\\(x_{i}=0\\)\u3001\\(i=j\\)\u3068\u306a\u308b\u3068\u3053\u308d\u3067\u306f\\(x_{j}=1\\)\u3068\u306a\u308b\u3053\u3068\u3092\u7528\u3044\u308b\u3068<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\exp\\left[ \\sum_{i=1}^{k}t_{i}x_{i} \\right]f(x_{j}) = \\exp[t_{j}]p_{j}<br>\\end{align}<\/div><br>\u3068\u306a\u308a\u307e\u3059\u3002<br>\u3000\u540c\u69d8\u306b\u3057\u3066\u7279\u6027\u95a2\u6570\u3082\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cf\">\uff1c\u7279\u6027\u95a2\u6570\u306e\u5b9a\u7fa9\uff1e<\/a>\u3068<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition\">\uff1c\u671f\u5f85\u5024\u306e\u5b9a\u7fa9\uff1e<\/a>\u304b\u3089<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\phi_{X}(t) &amp;= \\mathrm{E}\\left[ \\exp[itX] \\right] \\\\<br>&amp;= \\mathrm{E}\\left[ \\exp\\left[ \\sum_{\\ell=1}^{k}it_{\\ell}X_{\\ell} \\right] \\right] \\\\<br>&amp;= \\sum_{j=1}^{k} \\exp\\left[ \\sum_{\\ell=1}^{k}it_{\\ell}x_{\\ell} \\right]f(x_{j}) \\\\<br>&amp;= \\sum_{j=1}^{k} p_{j}\\exp\\left[ it_{j} \\right]<br>\\end{align}<\/div><br>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"has-text-align-right\">\u25a1<\/p>\n\n\n\n<h2><span id=\"i-5\">\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u3068\u95a2\u9023\u6df1\u3044\u5206\u5e03<\/span><\/h2>\n\n\n\n<p>\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u3068\u95a2\u9023\u6df1\u3044\u5206\u5e03\u3092\u56f3\u30fb\u8868\u3067\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002\u5404\u5206\u5e03\u306e\u8a73\u3057\u3044\u60c5\u5831\u306f\u8868\u306e\u4e2d\u306e\u30ea\u30f3\u30af\u304b\u3089\u304a\u9858\u3044\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"738\" height=\"514\" src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306e\u95a2\u4fc2\u30de\u30c3\u30d7.png\" alt=\"\" class=\"wp-image-2055\" srcset=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306e\u95a2\u4fc2\u30de\u30c3\u30d7.png 738w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306e\u95a2\u4fc2\u30de\u30c3\u30d7-300x209.png 300w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u306e\u95a2\u4fc2\u30de\u30c3\u30d7-320x223.png 320w\" sizes=\"(max-width: 738px) 100vw, 738px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/bernoulli-distribution\">\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3092\uff11\u56de\u884c\u3046\u3068\u304d\u306e\u5206\u5e03<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/categorical-distribution\">\u30ab\u30c6\u30b4\u30ea\u5206\u5e03<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">1\u56de\u306e\u8a66\u884c\u3067\\(k\\)\u901a\u308a\u306e\u30d1\u30bf\u30fc\u30f3\u306e\u4e2d\u304b\u3089\u3069\u308c\u304b\u304c\u5f97\u3089\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u8a66\u884c\u3092\u8868\u3059\u5206\u5e03<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/distribution\/bind\">\uff12\u9805\u5206\u5e03<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(n\\)\u56de\u306e\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3067\\(x\\)\u56de\u6210\u529f\u3059\u308b\u3068\u304d\u306e\u5206\u5e03<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/distribution\/dgeod\">\u5e7e\u4f55\u5206\u5e03<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3092\u8907\u6570\u56de\u884c\u3046\u4e0a\u3067\u3001\u521d\u3081\u3066\u6210\u529f\u3059\u308b\u307e\u3067\u306e<br>\u8a66\u884c\u56de\u6570\u3092\u8868\u3059\u5206\u5e03<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/distribution\/dhgeod\">\u8d85\u5e7e\u4f55\u5206\u5e03<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3092\u8907\u6570\u56de\u884c\u3063\u3066\u3044\u304f\u4e0a\u3067\u3001\u305d\u306e\u90fd\u5ea6\u6210\u529f\u78ba\u7387\u304c<br>\u5909\u5316\u3059\u308b\u5206\u5e03\uff08\u6709\u9650\u500b\u306e\u30a2\u30bf\u30ea\u304f\u3058\u306a\u3069\uff09<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/distribution\/nbiob\">\u8ca0\u306e\uff12\u9805\u5206\u5e03<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c\u3092\u8907\u6570\u56de\u884c\u3046\u4e0a\u3067\u3001\\(k\\)\u56de\u6210\u529f\u3059\u308b\u307e\u3067\u306e<br>\u5931\u6557\u3059\u308b\u56de\u6570\u3092\u8868\u3059\u5206\u5e03\uff08\\(k=1\\)\u306e\u5834\u5408\u3001\u5e7e\u4f55\u5206\u5e03\u306b\u306a\u308a\u307e\u3059\uff09<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/dmuld\">\u591a\u9805\u5206\u5e03<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u6210\u529f\u30fb\u5931\u6557\u306e\uff12\u7a2e\u985e\u3060\u3051\u3067\u306a\u304f\u3001\u8a66\u884c\u306e\u7d50\u679c\u304c<br>\u8907\u6570\u500b\u3042\u308b\u5834\u5408\u306e\u5206\u5e03\u3092\u8868\u3057\u307e\u3059<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/distribution\/dpoid\">\u30dd\u30a2\u30bd\u30f3\u5206\u5e03<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u6210\u529f\u78ba\u7387\u304c\u6975\u7aef\u306b\u5c0f\u3055\u304f\uff08\u3064\u307e\u308a\u6ec5\u591a\u306b\u8d77\u3053\u3089\u306a\u3044\uff09\u3001<br>\u8a66\u884c\u56de\u6570\u304c\u6975\u7aef\u306b\u5927\u304d\u3044\u5834\u5408\u306e\u5206\u5e03<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\u3000\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\uff08categorical distribution\uff09\uff08\u30ab\u30c6\u30b4\u30ea\u30ab\u30eb\u5206\u5e03\u30fb\u4e00\u822c\u5316\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u30fbmultinoulli\u5206\u5e03\uff09\u306f\u96e2 &#8230; <\/p>\n","protected":false},"author":1,"featured_media":801,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[76,74,72,84],"tags":[107,31,73,80,71,79],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/05\/PAK39_toumeinadice_TP_V.jpg","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2064"}],"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=2064"}],"version-history":[{"count":19,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2064\/revisions"}],"predecessor-version":[{"id":2146,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2064\/revisions\/2146"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/801"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=2064"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=2064"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=2064"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}