{"id":2356,"date":"2020-08-03T11:00:00","date_gmt":"2020-08-03T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=2356"},"modified":"2020-09-26T16:22:47","modified_gmt":"2020-09-26T07:22:47","slug":"exponential-distribution","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/exponential-distribution","title":{"rendered":"\u6307\u6570\u5206\u5e03"},"content":{"rendered":"\n\n\n\n\n<p>\u3000\u6307\u6570\u5206\u5e03\uff08exponential distribution\uff09\u306f\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u6307\u6570\u5206\u5e03\u306f\u3042\u308b\u4e8b\u8c61\u304c\u8d77\u3053\u3063\u3066\u304b\u3089\u3001\u6b21\u306b\u4e8b\u8c61\u304c\u767a\u751f\u3059\u308b\u307e\u3067\u306e\u671f\u9593\u3092\u3042\u3089\u308f\u3059\u78ba\u7387\u5206\u5e03\u306b\u306a\u308a\u307e\u3059\u3002<br>\u3000\u5177\u4f53\u7684\u306b\u306f\u3001\u3042\u308b\u751f\u7523\u30e9\u30a4\u30f3\u3067\u4f5c\u6210\u3055\u308c\u305f\u88fd\u54c1\u306e\u4e2d\u3067\u4e0d\u826f\u54c1\u304c\u767a\u898b\u3055\u308c\u3066\u304b\u3089\u3001\u6b21\u306b\u4e0d\u826f\u54c1\u304c\u767a\u898b\u3055\u308c\u308b\u307e\u3067\u306e\u671f\u9593\u304c\u6307\u6570\u5206\u5e03\u306b\u306a\u308a\u307e\u3059\u3002<br>\u3000\u6307\u6570\u5206\u5e03\u306f\u3001\u3042\u308b\u671f\u9593\u306e\u9593\u306b\u8d77\u3053\u308b\u4e8b\u8c61\u306e\u56de\u6570\u3092\\(\\lambda\\)\u56de\u3068\u3057\u305f\u3068\u304d\u3001\u4e8b\u8c61\u304c\u767a\u751f\u3057\u3066\u304b\u3089\u6b21\u306b\u4e8b\u8c61\u304c\u767a\u751f\u3059\u308b\u307e\u3067\u306e\u671f\u9593\u3092\\(X\\)\u3068\u3059\u308b\u3068\u3001\\(X\\)\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\lambda\\)\u306e\u6307\u6570\u5206\u5e03\u306b\u5f93\u3046\u3068\u3044\u3044\u3001\u8a18\u53f7\\(X\\sim Exp(\\lambda)\\)\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3000\u4f3c\u305f\u3088\u3046\u306a\u5206\u5e03\u306b\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u3061\u3089\u306f\u96e2\u6563\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3001\u3042\u308b\u4e00\u5b9a\u671f\u9593\u306e\u9593\u306b\u4e8b\u8c61\u304c\u767a\u751f\u3059\u308b\u56de\u6570\u3092\u8868\u3057\u307e\u3059\u3002\u8a73\u3057\u304f\u306f\u4e0b\u306e\u30ea\u30f3\u30af\u304b\u3089\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/poisson-distribution\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\uff08\u78ba\u7387\u95a2\u6570\uff09-100x100.png\" alt=\"\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u30dd\u30a2\u30bd\u30f3\u5206\u5e03<\/div>\n    <div class=\"blogcard_excerpt\">\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 class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\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> \u6307\u6570\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831<\/a><ul><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_2\">1.1<\/span> \u78ba\u7387\u5bc6\u5ea6\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> \u6307\u6570\u5206\u5e03\u306e\u7121\u8a18\u61b6\u6027<\/a><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">3<\/span> \u6307\u6570\u5206\u5e03\u3068\u30ac\u30f3\u30de\u5206\u5e03<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_1\">4<\/span> \u6307\u6570\u5206\u5e03\u3068\u30ef\u30a4\u30d6\u30eb\u5206\u5e03<\/a><\/li><li><a href=\"#i-6\"><span class=\"toc_number toc_depth_1\">5<\/span> \u6307\u6570\u5206\u5e03\u3068\u4e00\u69d8\u5206\u5e03<\/a><\/li><li><a href=\"#i-7\"><span class=\"toc_number toc_depth_1\">6<\/span> \u6307\u6570\u5206\u5e03\u3068\u30a2\u30fc\u30e9\u30f3\u5206\u5e03<\/a><\/li><li><a href=\"#i-8\"><span class=\"toc_number toc_depth_1\">7<\/span> \u6307\u6570\u5206\u5e03\u306e\u5dee<\/a><\/li><li><a href=\"#i-9\"><span class=\"toc_number toc_depth_1\">8<\/span> \u6307\u6570\u5206\u5e03\u3068\u30d1\u30ec\u30fc\u30c8\u5206\u5e03<\/a><\/li><li><a href=\"#i-10\"><span class=\"toc_number toc_depth_1\">9<\/span> \u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a\uff08\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5\u30fb\u6700\u5c24\u6cd5\uff09<\/a><\/li><\/ul><\/div>\n<h2><span id=\"i\">\u6307\u6570\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<figure class=\"wp-block-table\">\n<table style=\"width: 100%; height: 922px;\">\n<tbody>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\">\u30d1\u30e9\u30e1\u30fc\u30bf<\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\(0 &lt; \\lambda\\)<\/td>\n<\/tr>\n<tr style=\"height: 56px;\">\n<td style=\"width: 29.6413%; height: 56px;\">\u78ba\u7387\u5909\u6570\u306e\u7bc4\u56f2<\/td>\n<td style=\"width: 70.1863%; height: 56px;\">\\(0\\leq x \\)<\/td>\n<\/tr>\n<tr style=\"height: 56px;\">\n<td style=\"width: 29.6413%; height: 56px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cumulative-distribution-function\">\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/a><\/td>\n<td style=\"width: 70.1863%; height: 56px;\">\\(\\displaystyle 1-\\exp\\left[-\\lambda x\\right]\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/probability-function\">\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570<\/a><\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\(\\displaystyle\\lambda\\exp\\left[ -\\lambda x \\right]\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\">\u9006\u751f\u5b58\u95a2\u6570<br \/>\uff08\u78ba\u7387\\(p\\)\uff09<\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\(\\displaystyle-\\frac{\\lambda}\\log(1-p)\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\">\u751f\u5b58\u95a2\u6570<\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\(\\displaystyle\\exp\\left[ -\\lambda x \\right]\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\">\u9006\u751f\u5b58\u95a2\u6570<br \/>\uff08\u78ba\u7387\\(p\\)\uff09<\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\(\\displaystyle-\\frac{1}{\\lambda}\\log p\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\">\u5371\u967a\u5ea6\u95a2\u6570<\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\(\\displaystyle\\lambda\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\">\u7d2f\u7a4d\u5371\u967a\u5ea6\u95a2\u6570<\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\(\\displaystyle\\lambda x\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mgf\">\u7a4d\u7387\u6bcd\u95a2\u6570<\/a><\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\(\\displaystyle\\frac{\\lambda}{\\lambda-t}\\ \\ \\ t&lt; \\lambda\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 31px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cf\">\u7279\u6027\u95a2\u6570<\/a><\/td>\n<td style=\"width: 70.1863%; height: 31px;\">\\(\\displaystyle \\frac{\\lambda}{\\lambda-it}\\)<\/td>\n<\/tr>\n<tr style=\"height: 56px;\">\n<td style=\"width: 29.6413%; height: 63px;\"><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: 70.1863%; height: 63px;\">\\( \\displaystyle-\\log(1-\\frac{t}{\\lambda}) \\)<\/td>\n<\/tr>\n<tr style=\"height: 56px;\">\n<td style=\"width: 29.6413%; height: 56px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cgf\">\\(r\\)\u6b21\u30ad\u30e5\u30e0\u30e9\u30f3\u30c8<\/a><\/td>\n<td style=\"width: 70.1863%; height: 56px;\">\\( \\displaystyle(r-1)!\\left(\\frac{1}{\\lambda}\\right)^{r},\\ \\ \\ r&gt;1 \\)<\/td>\n<\/tr>\n<tr style=\"height: 56px;\">\n<td style=\"width: 29.6413%; height: 56px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/moment\">\\(r\\)\u6b21\u30e2\u30fc\u30e1\u30f3\u30c8\uff08\u539f\u70b9\u307e\u308f\u308a\uff09<\/a><\/td>\n<td style=\"width: 70.1863%; height: 56px;\">\\( \\displaystyle r!\\left(\\frac{1}{\\lambda}\\right)^{r}\\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mean-definition\">\u671f\u5f85\u5024<\/a><\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\( \\displaystyle\\frac{1}{\\lambda} \\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/variance\">\u5206\u6563<\/a><\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\( \\displaystyle\\frac{1}{\\lambda^{2}} \\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/05242107-2\">\u5e73\u5747\u504f\u5dee<\/a><\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\( \\displaystyle\\frac{2}{e\\lambda} \\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\">\u4e2d\u4f4d\u6570<\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\( \\displaystyle\\frac{1}{\\lambda}\\log 2 \\)<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/05231022\">\u30e2\u30fc\u30c9<\/a><\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\( 0 \\)<\/td>\n<\/tr>\n<tr style=\"height: 100px;\">\n<td style=\"width: 29.6413%; height: 100px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/skewness\">\u6b6a\u5ea6<\/a><\/td>\n<td style=\"width: 70.1863%; height: 100px;\">\n<p>\\(2\\)<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 36px;\">\n<td style=\"width: 29.6413%; height: 36px;\"><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/kurtosis\">\u5c16\u5ea6<\/a><\/td>\n<td style=\"width: 70.1863%; height: 36px;\">\\( 6 \\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\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\/cexpd-mv\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09-100x100.png\" alt=\"\u6307\u6570\u5206\u5e03\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3067\u89e3\u8aac\u3011\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u6307\u6570\u5206\u5e03\u306e\u671f\u5f85\u5024\u30fb\u5206\u6563\u306e\u6c42\u3081\u65b9\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\u2605\u2606\u2606\u2606 \u3053\u306e\u8a18\u4e8b\u3067\u306f\u6307\u6570\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\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\/cexpd-mc\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\uff09-100x100.png\" alt=\"\u6307\u6570\u5206\u5e03\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u30fb\u7279\u6027\u95a2\u6570\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3011\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u6307\u6570\u5206\u5e03\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u30fb\u7279\u6027\u95a2\u6570\u306e\u6c42\u3081\u65b9\u3010\u8a3c\u660e\u4ed8\u304d\u3011<\/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\u6307\u6570\u5206\u5e03\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\u6c42\u3081\u65b9\u304c\u5206\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n<h3><span id=\"i-2\">\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/span><\/h3>\n\n\n\n<p>\\(\\lambda=0.2,\\ 0.5,\\ 1,\\ 2,\\ 3\\)\u306b\u5bfe\u5fdc\u3059\u308b\u6307\u6570\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3001\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=\"980\" height=\"617\" src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09.png\" alt=\"\" class=\"wp-image-2359\" srcset=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09.png 980w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09-300x189.png 300w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09-768x484.png 768w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09-320x201.png 320w\" sizes=\"(max-width: 980px) 100vw, 980px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" width=\"980\" height=\"617\" src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\uff09.png\" alt=\"\" class=\"wp-image-2360\" srcset=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\uff09.png 980w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\uff09-300x189.png 300w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\uff09-768x484.png 768w, https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\uff09-320x201.png 320w\" sizes=\"(max-width: 980px) 100vw, 980px\" \/><\/figure>\n\n\n\n<h2><span id=\"i-3\">\u6307\u6570\u5206\u5e03\u306e\u7121\u8a18\u61b6\u6027<\/span><\/h2>\n\n\n\n<p>\u5e7e\u4f55\u5206\u5e03\u3068\u540c\u69d8\u306b\u3001\u6307\u6570\u5206\u5e03\u3082\u7121\u8a18\u61b6\u6027\u3068\u3044\u3046\u6027\u8cea\u3092\u6301\u3061\u307e\u3059\u3002\u7121\u8a18\u61b6\u6027\u3068\u306f\u3001\u904e\u53bb\u306b\u8d77\u3053\u3063\u305f\u7d50\u679c\u306b\u3088\u3063\u3066\u3001\u4e8b\u8c61\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u306f\u5909\u5316\u3057\u306a\u3044\u3068\u3044\u3046\u6027\u8cea\u306b\u306a\u308a\u307e\u3059\u3002\u5f0f\u3067\u66f8\u304f\u3068<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\mathrm{P}(X&gt;n+m|X&gt;m)=\\mathrm{P}(X&gt;n)<br>\\end{align}<\/div><br>\u3068\u306a\u308a\u307e\u3059\u3002<br>\u3000\u5177\u4f53\u7684\u306b\u306f\u3001\u3042\u308b\u88fd\u54c1\u3092\u4f5c\u308b\u6a5f\u68b0\u306f100\u500b\u306b1\u500b\u306e\u5272\u5408\u3067\u4e0d\u826f\u54c1\u304c\u767a\u898b\u3055\u308c\u308b\u3082\u306e\u3060\u3068\u3057\u307e\u3059\u3002\u4eca\u3001\u3053\u306e\u6a5f\u68b0\u3067100\u500b\u88fd\u54c1\u3092\u4f5c\u6210\u3057\u3001\u4e0d\u826f\u54c1\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u4e0d\u826f\u54c1\u304c\u898b\u3064\u304b\u308b\u307e\u3067\u306b\u304b\u304b\u308b\u88fd\u54c1\u306e\u500b\u6570\u306f\u3001\u300c\u4e0d\u826f\u54c1\u304c\u898b\u3064\u304b\u3063\u3066\u304b\u3089\u6b21\u306e\u4e0d\u826f\u54c1\u304c\u767a\u898b\u3055\u308c\u308b\u307e\u3067\u306e\u88fd\u54c1\u306e\u500b\u6570\u300d\u306f\u78ba\u7387\u7684\u306b\u540c\u3058\u306b\u306a\u308a\u307e\u3059\u3002<br>\u3000\u30bd\u30fc\u30b7\u30e3\u30eb\u30b2\u30fc\u30e0\u306e\u30ac\u30c1\u30e3\u3067\u8a00\u3046\u3068\u3001S\u30e9\u30f3\u30ad\u30e3\u30e9\u304c\u51fa\u3066\u304d\u3066\u304b\u3089\u6b21\u306bS\u30e9\u30f3\u30ad\u30e3\u30e9\u304c\u51fa\u308b\u307e\u3067\u306b\u304b\u304b\u308b\u56de\u6570\u3068\u3001100\u56de\u9023\u7d9a\u3067\u30cf\u30ba\u30ec\u7d9a\u3051\u3066\u304b\u3089S\u30e9\u30f3\u30ad\u30e3\u30e9\u304c\u51fa\u308b\u307e\u3067\u306b\u304b\u304b\u308b\u56de\u6570\u306f\u78ba\u7387\u7684\u306b\u540c\u3058\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u3000\u307e\u3068\u3081\u308b\u3068\u3001\u300c\u4eca\u81ea\u5206\u306f\u30cf\u30ba\u30ec\u7d9a\u3051\u3066\u3044\u308b\u304b\u3089\u3001\u30a2\u30bf\u30ea\u3092\u5f15\u304f\u78ba\u7387\u306f\u9ad8\u304f\u306a\u3063\u3066\u3044\u308b\u300d\u3068\u3044\u3046\u8003\u3048\u65b9\u306f\u3001\u6307\u6570\u5206\u5e03\u3084\u5e7e\u4f55\u5206\u5e03\u3067\u306f\u771f\u3063\u5411\u304b\u3089\u5426\u5b9a\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-4\">\u6307\u6570\u5206\u5e03\u3068\u30ac\u30f3\u30de\u5206\u5e03<\/span><\/h2>\n\n\n\n<p>\u3000\u30ac\u30f3\u30de\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\sim Gam(1,\\lambda)\\)\u306f\u3001\u6307\u6570\u5206\u5e03\\(X\\sim Exp(\\lambda)\\)\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u306f\u7a4d\u7387\u6bcd\u95a2\u6570\u3092\u4f7f\u3063\u3066\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002\u30ac\u30f3\u30de\u5206\u5e03\\(Gam(\\alpha,\\beta)\\)\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u306f<br><div style=\"overflow-x: auto;\">\\begin{align}<br>M_{X}(t) = (1-\\beta t)^{-\\alpha}<br>\\end{align}<\/div><br>\u3068\u306a\u308b\u3053\u3068\u304b\u3089\u3001\\(\\alpha=1,\\beta=\\frac{1}{\\lambda}\\)\u3067\u7a4d\u7387\u6bcd\u95a2\u6570\u3092\u66f8\u304d\u63db\u3048\u308b\u3068\u3001<br><div style=\"overflow-x: auto;\">\\begin{align}<br>M_{X}(t) = \\left(1-\\frac{t}{\\lambda} \\right)^{-1}<br>\\end{align}<\/div><br>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u3053\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\lambda\\)\u306e\u6307\u6570\u5206\u5e03\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u3068\u4e00\u81f4\u3059\u308b\u3053\u3068\u304b\u3089\u3001<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mgf\">\u7a4d\u7387\u6bcd\u95a2\u6570\u306e\u6027\u8cea<\/a>\u304b\u3089\u6307\u6570\u5206\u5e03\u306b\u5f93\u3046\u3053\u3068\u304c\u308f\u304b\u308a\u3042\u307e\u3059\u3002<\/p>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mgf\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/9fc17caf-9cad-4670-b857-eb43ec911ab9-100x100.png\" alt=\"\u7a4d\u7387\u6bcd\u95a2\u6570\u3068\u306f\u3010\u5b9a\u7fa9\u3068\u6027\u8cea\u3092\u89e3\u8aac\u3011\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u7a4d\u7387\u6bcd\u95a2\u6570\u3068\u306f\u3010\u5b9a\u7fa9\u3068\u6027\u8cea\u3092\u89e3\u8aac\u3011<\/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 \u539f\u70b9\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u6c42\u3081\u308b\u305f\u3081\u306e\u95a2\u6570\u306b\u7a4d\u7387\u6bcd\u95a2\u6570\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002\u7a4d\u7387\u6bcd\u95a2\u6570\u3092\u7528\u3044\u308c\u3070\u671f\u5f85\u5024\u3084\u5206\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-5\">\u6307\u6570\u5206\u5e03\u3068\u30ef\u30a4\u30d6\u30eb\u5206\u5e03<\/span><\/h2>\n\n\n\n<p>\u3000\u30ef\u30a4\u30d6\u30eb\u5206\u5e03\\(W(\\phi,\\gamma)\\)\u306b\u3064\u3044\u3066\u3001\\(\\gamma=1\\)\u306e\u5834\u5408\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\phi\\)\u306e\u6307\u6570\u5206\u5e03\u3068\u4e00\u81f4\u3057\\(Exp(1\/\\phi)=W(\\phi,1)\\)\u3068\u306a\u308a\u307e\u3059\u3002<br>\u3000\u9006\u306b\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\lambda\\)\u306e\u6307\u6570\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\sim Exp(\\lambda)\\)\u306b\u3064\u3044\u3066\u3001\\(Y=\\lambda(\\frac{X}{\\lambda})^{\\frac{1}{\\gamma}}\\)\u3068\u5909\u63db\u3059\u308b\u3068\u3001\\(Y\\)\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\\(1\/\\lambda,\\gamma\\)\u306e\u30ef\u30a4\u30d6\u30eb\u5206\u5e03\\(Y\\sim W(1\/\\lambda,\\gamma)\\)\u306b\u5f93\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-6\">\u6307\u6570\u5206\u5e03\u3068\u4e00\u69d8\u5206\u5e03<\/span><\/h2>\n\n\n\n<p>\u3000\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\lambda\\)\u306e\u6307\u6570\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X\\sim Exp(\\lambda)\\)\u3068\u3001\u533a\u9593\\([0,1]\\)\u306e\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(Y\\sim U(0,1)\\)\u3068\u6b21\u306e\u3088\u3046\u306a\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>X = -\\frac{1}{\\lambda}\\log Y<br>\\end{align}<\/div><\/p>\n\n\n\n\n  <div class=\"blogcard\">\n  <a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/continuous-uniform-distribution\">\n   <div class=\"blogcard_thumbnail\"><img src=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/\u4e00\u69d8\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09-100x100.png\" alt=\"\u4e00\u69d8\u5206\u5e03\uff08\u9023\u7d9a\u578b\uff09\" width=\"90\" height=\"90\" \/><\/div>\n   <div class=\"blogcard_content\">\n    <div class=\"blogcard_title\">\u4e00\u69d8\u5206\u5e03\uff08\u9023\u7d9a\u578b\uff09<\/div>\n    <div class=\"blogcard_excerpt\">\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\u306f\u5225\u540d\u3001\u77ed\u5f62\u5206\u5e03\uff08rectangular di\u2026<\/div>\n   <\/div>\n   <div class=\"clear\"><\/div>\n  <\/a>\n  <\/div>\n\n\n\n<p> <\/p>\n\n\n\n<h2><span id=\"i-7\">\u6307\u6570\u5206\u5e03\u3068\u30a2\u30fc\u30e9\u30f3\u5206\u5e03<\/span><\/h2>\n\n\n\n<p>\u3000\\(X_{1},\\cdots,X_{n}\\)\u304c\u4e92\u3044\u306b\u72ec\u7acb\u306b\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\lambda\\)\u306e\u6307\u6570\u5206\u5e03\\(X_{i}\\sim Exp(\\lambda),\\ i=1,\\cdots,n\\)\u306b\u5f93\u3046\u3068\u304d\u3001\u3053\u306e\u78ba\u7387\u5909\u6570\u306e\u548c\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\alpha=n,\\ \\beta=\\frac{1}{\\lambda}\\)\u306e\u30a2\u30fc\u30e9\u30f3\u5206\u5e03\u306b\u5f93\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-8\">\u6307\u6570\u5206\u5e03\u306e\u5dee<\/span><\/h2>\n\n\n\n<p>\u3000\uff12\u3064\u306e\u72ec\u7acb\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\lambda\\)\u306e\u6307\u6570\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\\(X_{1},X_{2}\\sim Exp(\\lambda)\\)\u306e\u5dee\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\frac{1}{\\lambda}\\)\u306e\u30e9\u30d7\u30e9\u30b9\u5206\u5e03\u306b\u5f93\u3044\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>X_{1}-X_{2}\\sim Laplace(1\/\\lambda)<br>\\end{align}<\/div><\/p>\n\n\n\n<p>\u3000<\/p>\n\n\n\n<h2><span id=\"i-9\">\u6307\u6570\u5206\u5e03\u3068\u30d1\u30ec\u30fc\u30c8\u5206\u5e03<\/span><\/h2>\n\n\n\n<p>\u3000\u30d1\u30e9\u30e1\u30fc\u30bf\\(\\lambda\\)\u306e\u6307\u6570\u5206\u5e03\u306b\u5f93\u3046\u3001\u78ba\u7387\u5909\u6570\\(X\\sim Exp(\\lambda)\\)\u3092\u5909\u6570\u5909\u63db\\(Y= ae^{x}\\)\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\\(a,\\lambda\\)\u306e\u30d1\u30ec\u30fc\u30c8\u5206\u5e03\u306b\u5f93\u3044\u307e\u3059\u3002<br><div style=\"overflow-x: auto;\">\\begin{align}<br>Y \\sim Pareto\\left(a,\\lambda\\right)<br>\\end{align}<\/div><\/p>\n\n\n\n<p> <\/p>\n\n\n\n<h2><span id=\"i-10\">\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a\uff08\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5\u30fb\u6700\u5c24\u6cd5\uff09<\/span><\/h2>\n\n\n\n<p> \u6700\u5c24\u6cd5\u30fb\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5\u306b\u3088\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<ul><li>\u6700\u5c24\u6cd5<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\widehat{\\lambda} = \\bar{X}<br>\\end{align}<\/div><\/li><li>\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5<br><div style=\"overflow-x: auto;\">\\begin{align}<br>\\widehat{\\lambda} = \\sqrt{\\frac{1}{n}\\sum_{i=1}^{n}(X_{i}-\\bar{X})^{2}}<br>\\end{align}<\/div><\/li><\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3000\u6307\u6570\u5206\u5e03\uff08exponential distribution\uff09\u306f\u9023\u7d9a\u578b\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\u6307\u6570\u5206\u5e03\u306f\u3042\u308b\u4e8b\u8c61\u304c\u8d77\u3053\u3063\u3066\u304b\u3089\u3001\u6b21\u306b\u4e8b\u8c61\u304c\u767a\u751f\u3059\u308b\u307e &#8230; <\/p>\n","protected":false},"author":1,"featured_media":2359,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[84],"tags":[112,71],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6307\u6570\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09.png","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2356"}],"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=2356"}],"version-history":[{"count":24,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2356\/revisions"}],"predecessor-version":[{"id":3154,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/2356\/revisions\/3154"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/2359"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=2356"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=2356"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=2356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}