{"id":1652,"date":"2020-07-04T11:00:00","date_gmt":"2020-07-04T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=1652"},"modified":"2020-07-11T13:14:26","modified_gmt":"2020-07-11T04:14:26","slug":"discrete-uniform-distribution","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/discrete-uniform-distribution","title":{"rendered":"\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09"},"content":{"rendered":"\n\n\n\n\n<p>\u4e00\u69d8\u5206\u5e03\uff08uniform distribution\uff09\u306f\u6700\u3082\u30b7\u30f3\u30d7\u30eb\u306a\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\)\u3092\u30d1\u30e9\u30e1\u30fc\u30bf\\(n\\)\uff08\u305f\u3060\u3057\\(n\\)\u306f\u6b63\u306e\u5b9f\u6570\uff09\u3092\u7528\u3044\u3066\u3001\u8a18\u53f7\\(X\\sim U(n)\\)\u3067\u3088\u304f\u8868\u3055\u308c\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> \u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u57fa\u672c\u60c5\u5831<\/a><ul><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_2\">1.1<\/span> \u78ba\u7387\u95a2\u6570\u3068\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/a><\/li><\/ul><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">2<\/span> \u975e\u6574\u6570\u306e\u4e00\u69d8\u5206\u5e03<\/a><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">3<\/span> \u4e71\u6570\u306e\u767a\u751f\u65b9\u6cd5<\/a><\/li><\/ul><\/div>\n<h2><span id=\"i\">\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u57fa\u672c\u60c5\u5831<\/span><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>\u30d1\u30e9\u30e1\u30fc\u30bf<\/td><td>\\(n\\)<\/td><\/tr><tr><td>\u78ba\u7387\u5909\u6570\u306e\u7bc4\u56f2<\/td><td>\\(0\\leq x \\leq n\\)\u3000\u3000\\(x\\)\u306f\u6574\u6570<\/td><\/tr><tr><td><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cumulative-distribution-function\">\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/a><\/td><td>\\(\\displaystyle\\frac{x+1}{n+1}\\)<\/td><\/tr><tr><td><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/probability-function\">\u78ba\u7387\u95a2\u6570<\/a><\/td><td>\\(\\displaystyle\\frac{1}{n+1}\\)<\/td><\/tr><tr><td>\u9006\u5206\u5e03\u95a2\u6570\uff08\u78ba\u7387\\(p\\)\uff09<\/td><td>\\(p(n+1)-1\\)<\/td><\/tr><tr><td>\u9006\u751f\u5b58\u95a2\u6570\uff08\u78ba\u7387\\(p\\)\uff09<\/td><td>\\(n-p(n+1)\\)<\/td><\/tr><tr><td>\u5371\u967a\u5ea6\u95a2\u6570<\/td><td>\\(\\displaystyle\\frac{1}{n-x}\\)<\/td><\/tr><tr><td><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mgf\">\u7a4d\u7387\u6bcd\u95a2\u6570<\/a><\/td><td>\\(\\displaystyle\\frac{ 1-\\exp[t(n+1)] }{(n+1)(1-\\exp[t])}\\)<\/td><\/tr><tr><td><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cf\">\u7279\u6027\u95a2\u6570<\/a><\/td><td>\\(\\displaystyle\\frac{1-\\exp[it(n+1)]}{(1-\\exp[it])(n+1)}\\)<\/td><\/tr><tr><td><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/moment\">\u30e2\u30fc\u30e1\u30f3\u30c8\uff08\u539f\u70b9\u307e\u308f\u308a\uff09<\/a><\/td><td><div style=\"overflow-x: auto;\">\\begin{align}<br>\\left\\{<br>\\begin{array}{ccc}<br>&amp; 1\u6b21\uff08\u671f\u5f85\u5024\uff09 &amp; \\displaystyle\\frac{n}{2} \\\\<br>&amp; 2\u6b21 &amp; \\displaystyle\\frac{n(2n+1)}{6} \\\\<br>&amp; 3\u6b21 &amp; \\displaystyle\\frac{n^{2}(n+1)}{4}  <br>\\end{array}\\right.<br>\\end{align}<\/div><\/td><\/tr><tr><td><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition\">\u671f\u5f85\u5024<\/a><\/td><td>\\( \\displaystyle\\frac{n}{2} \\)<\/td><\/tr><tr><td><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/variance\">\u5206\u6563<\/a><\/td><td>\\(\\displaystyle\\frac{n(n+2)}{12} \\)<\/td><\/tr><tr><td><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/skewness\">\u6b6a\u5ea6<\/a><\/td><td>\\(0\\)<\/td><\/tr><tr><td><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/kurtosis\">\u5c16\u5ea6<\/a><\/td><td>\\( \\displaystyle\\frac{3}{5}\\left[ 3-\\frac{4}{n(n+2)} \\right] \\)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3>\u8a3c\u660e\u4e00\u89a7<\/h3>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/dud-mv\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570-100x100.png\" alt=\"\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u671f\u5f85\u5024\u3068\u5206\u6563\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u671f\u5f85\u5024\u3068\u5206\u6563\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011<\/div>\n    <div class=\"blogcard_excerpt\">\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u5927\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606 \u3053\u306e\u8a18\u4e8b\u3067\u306f\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\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\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/dud-mc\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570-100x100.png\" alt=\"\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u30fb\u7279\u6027\u95a2\u6570\u306e\u6c42\u3081\u65b9\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u30fb\u7279\u6027\u95a2\u6570\u306e\u6c42\u3081\u65b9<\/div>\n    <div class=\"blogcard_excerpt\">\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\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u30fb\u7279\u6027\u95a2\u6570\u3092\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u7a4d\u7387\u6bcd\u95a2\u6570\u30fb\u7279\u6027\u95a2\u6570\u306e\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n<h3><span id=\"i-2\">\u78ba\u7387\u95a2\u6570\u3068\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/span><\/h3>\n\n\n\n<p>\\(n=10\\)\u306e\u3068\u304d\u306e\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u306e\u78ba\u7387\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"973\" height=\"612\" src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570.png\" alt=\"\" class=\"wp-image-1657\" srcset=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570.png 973w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570-300x189.png 300w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570-768x483.png 768w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570-320x201.png 320w\" sizes=\"(max-width: 973px) 100vw, 973px\" \/><\/figure>\n\n\n\n<p> \\(n=10,\\ n=20\\)\u306e\u3068\u304d\u306e\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"971\" height=\"611\" src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570.png\" alt=\"\" class=\"wp-image-1658\" srcset=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570.png 971w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570-300x189.png 300w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570-768x483.png 768w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570-320x201.png 320w\" sizes=\"(max-width: 971px) 100vw, 971px\" \/><\/figure>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-3\">\u975e\u6574\u6570\u306e\u4e00\u69d8\u5206\u5e03<\/span><\/h2>\n\n\n\n<p>\u78ba\u7387\u5909\u6570\\(X\\)\u304c\u975e\u8ca0\u306e\u6574\u6570\u3067\u306f\u306a\u304f\u3001\u78ba\u7387\u95a2\u6570<br><div style=\"overflow-x: auto;\">\\begin{align}<br>f(X=a+jh) = \\frac{1}{n+1}\\ \\ \\ \\ j=0,1,\\cdots,n<br>\\end{align}<\/div><br>\u3092\u3082\u3064\u5834\u5408\u3082\u96e2\u6563\u578b\u306e\u4e00\u69d8\u5206\u5e03\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\\(X\\)\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\\(M_{X}(t)\\)\u306f\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>M_{X}(t) = \\frac{ \\exp[ta](\\exp[(n+1)th]-1) }{ (n+1)(\\exp[th]-1) }<br>\\end{align}<\/div><\/p>\n\n\n\n<p> <\/p>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-4\">\u4e71\u6570\u306e\u767a\u751f\u65b9\u6cd5<\/span><\/h2>\n\n\n\n<p>\\(i,\\ j\\)\u3092\\(i&lt;j\\)\u3092\u6e80\u305f\u3059\u3001\u6574\u6570\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\\(i\\leq x\\leq j\\)\u306e\u9593\u3092\u3068\u308b\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u306f\u6b21\u306e\u624b\u9806\u3067\u4f5c\u6210\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<ol><li>\u307e\u305a\\(U\\sim U(0,\\ 1)\\)\u3092\u767a\u751f\u3055\u305b\u307e\u3059\u3002<\/li><li>\\(X=i+[(j-i+1)U]\\)\u3068\u3057\u307e\u3059\u3002\u305f\u3060\u3057\\([\\ast]\\)\u306f\\(\\ast\\)\u3092\u8d8a\u3048\u306a\u3044\u6700\u5927\u6574\u6570\u3092\u8868\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u306e\\(X\\)\u3092\u4e71\u6570\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\u3002<\/li><\/ol>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e00\u69d8\u5206\u5e03\uff08uniform distribution\uff09\u306f\u6700\u3082\u30b7\u30f3\u30d7\u30eb\u306a\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\)\u3092\u30d1\u30e9\u30e1\u30fc\u30bf\\(n &#8230; <\/p>\n","protected":false},"author":1,"featured_media":1657,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[84],"tags":[97,71],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u96e2\u6563\u578b\uff09\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570.png","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1652"}],"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=1652"}],"version-history":[{"count":11,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1652\/revisions"}],"predecessor-version":[{"id":1942,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1652\/revisions\/1942"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/1657"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=1652"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=1652"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=1652"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}