{"id":1185,"date":"2020-06-18T11:00:00","date_gmt":"2020-06-18T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=1185"},"modified":"2020-06-30T21:16:47","modified_gmt":"2020-06-30T12:16:47","slug":"moment","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/moment","title":{"rendered":"\u30e2\u30fc\u30e1\u30f3\u30c8\u3068\u306f\u3010\u5b9a\u7fa9\u304b\u3089\u89e3\u8aac\u3011"},"content":{"rendered":"\n<p class=\"has-text-align-right\"><span style=\"text-decoration: underline;\">\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u9ad8\u6821\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2605\u2606\u2606\u2606<\/span><\/p>\n\n\n\n\n\n\n\n<p>\u5e73\u5747\u3084\u5206\u6563\u306a\u3069\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u304c\u30e2\u30fc\u30e1\u30f3\u30c8\uff08\u7a4d\u7387\uff09\u3067\u3059\u3002\u30e2\u30fc\u30e1\u30f3\u30c8\u306b\u306f[\u539f\u70b9\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8]\u3068[\u5e73\u5747\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8]\u306a\u3069\u304c\u3042\u308a\u307e\u3059\u3002\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u6c42\u3081\u308b\u306e\u306f\u5bb9\u6613\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u30e2\u30fc\u30e1\u30f3\u30c8\u304c\u6301\u3064\u60c5\u5831\u306f\u304b\u306a\u308a\u5927\u304d\u3044\u3067\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u30e2\u30fc\u30e1\u30f3\u30c8\u306e\u5b9a\u7fa9\u306b\u3064\u3044\u3066\u6271\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2>\u30e2\u30fc\u30e1\u30f3\u30c8\uff08\u7a4d\u7387\uff09\u306e\u5b9a\u7fa9<\/h2>\n\n\n\n<div style=\"display: inline-block; background: #33cc33; padding: 5px 10px; color: #ffffff; border-radius: 5px 5px 0 0;\"><strong>\u30e2\u30fc\u30e1\u30f3\u30c8(\u7a4d\u7387\u3000moment)<\/strong><\/div>\n<div style=\"background: #ffffea; padding: 10px; border: 2px solid #33cc33;\">\u30e2\u30fc\u30e1\u30f3\u30c8\u306b\u306f\u300c\u539f\u70b9\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u300d\u3068\u300c\u5e73\u5747\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u300d\u304c\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<br \/><strong>\u30fb\u30e2\u30fc\u30e1\u30f3\u30c8<\/strong><br \/>\u3000\u78ba\u7387\u5909\u6570\\(X\\)\u306e\\(k\\)\u6b21\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\uff08\u539f\u70b9\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\uff09\u3092\\(\\mu^{\\prime}_{k}\\)\u3067\u8868\u3057\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002$$\\mu^{\\prime}_{k} = \\mathrm{E}\\left[ X^{k} \\right]$$ <br \/><strong>\u30fb\u4e2d\u5fc3\u30e2\u30fc\u30e1\u30f3\u30c8<\/strong><br \/>\u3000\u78ba\u7387\u5909\u6570\\(X\\)\u306e\\(k\\)\u6b21\u306e\u4e2d\u5fc3\u30e2\u30fc\u30e1\u30f3\u30c8\uff08\u5e73\u5747\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\uff09\u3092\\(\\mu_{k}\\)\u3067\u8868\u3057\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002$$\\mu_{k} = \\mathrm{E}\\left[ (X-\\mathrm{E}[X])^{k} \\right]$$<br \/><strong>\u30fb\u4efb\u610f\u306e\u70b9\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8<br \/><\/strong>\u3000\u30e2\u30fc\u30e1\u30f3\u30c8\u306f\u539f\u70b9\u3001\u4e2d\u5fc3\u3060\u3051\u3067\u306a\u304f\u4efb\u610f\u306e\u70b9\u306e\u307e\u308f\u308a\u3067\u3082\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002\u4efb\u610f\u306e\u70b9\\(a\\)\u306e\u307e\u308f\u308a\u306e\\(k\\)\u6b21\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\\(\\mu^{\\prime}_{k}(a) \\)\u3067\u8868\u3057\u3001\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002$$\\mu_{k}^{\\prime}(a) = \\mathrm{E}\\left[ (X-a)^{k} \\right]$$<br \/><strong>\u30fb\u7d76\u5bfe\u30e2\u30fc\u30e1\u30f3\u30c8<\/strong><br \/>\u3000\u78ba\u7387\u5909\u6570\\(X\\)\u306e\\(a\\)\u306e\u307e\u308f\u308a\u306e\\(k\\)\u6b21\u306e\u7d76\u5bfe\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\\(\\upsilon_{k}^{\\prime}(a)\\)\u3067\u8868\u3057\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002$$\\upsilon_{k}^{\\prime}(a) = \\mathrm{E}\\left[ \\left|X-a\\right|^{k} \\right]$$<br \/><strong>\u30fb\u968e\u4e57\u30e2\u30fc\u30e1\u30f3\u30c8<br \/><\/strong>\u3000\u78ba\u7387\u5909\u6570\\(X\\)\u306e\\(k\\)\u6b21\u306e\u968e\u4e57\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\\(\\mu_{[k]}^{\\prime}\\)\u3067\u8868\u3057\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002$$\\mu_{[k]}^{\\prime} = \\mathrm{E}\\left[ X(X-1)(X-2)\\cdots(X-k+1) \\right]$$<\/div>\n<p>\u00a0<\/p>\n\n\n\n<div class=\"wp-block-liquid-speech-balloon liquid-speech-balloon-wrap liquid-speech-balloon-00  liquid-speech-balloon-short\"><div class=\"liquid-speech-balloon-avatar\"><\/div><div class=\"liquid-speech-balloon-text\" style=\"border-color:#d6ebf8;background-color:#d6ebf8;color:#000000\"><p>\u30e2\u30fc\u30e1\u30f3\u30c8\u306b\u306f\u3055\u307e\u3056\u307e\u306a\u7a2e\u985e\u304c\u3042\u308a\u307e\u3059\u304c\u3001<br>\u7279\u306b<strong>\u300c\u30e2\u30fc\u30e1\u30f3\u30c8\u300d\u300c\u4e2d\u5fc3\u30e2\u30fc\u30e1\u30f3\u30c8\u300d<\/strong>\u304c\u91cd\u8981\u3067\u3059\u3002<br>\u30e2\u30fc\u30e1\u30f3\u30c8\u3001\u4e2d\u5fc3\u30e2\u30fc\u30e1\u30f3\u30c8\u306e\u5b9a\u7fa9\u304b\u3089\u6b21\u306e\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\n\n\n\n<ul><li>\\(1\\)\u6b21\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\\(\\mu_{1}^{\\prime}\\)\u306f\u671f\u5f85\u5024\u3092\u8868\u3057\u307e\u3059\u3002<\/li><li>\\(2\\)\u6b21\u306e\u4e2d\u5fc3\u30e2\u30fc\u30e1\u30f3\u30c8\\(\\mu_{2}\\)\u306f\u5206\u6563\u3092\u8868\u3057\u307e\u3059\u3002<\/li><\/ul>\n\n\n\n<p>\u3053\u308c\u3089\u306b\u52a0\u3048\u3066\u3001\\(3\\)\u6b21\u306e\u4e2d\u5fc3\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u7528\u3044\u305f\u6b6a\u5ea6\u3001\\(4\\)\u6b21\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u7528\u3044\u305f\u5c16\u5ea6\u3068\u547c\u3070\u308c\u308b\u6307\u6a19\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<script async=\"\" src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\n<!-- \u6a2a\u9577\u5e83\u544a -->\n<ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1927349886186426\" data-ad-slot=\"2608642117\" data-ad-format=\"auto\" 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href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/pgf\">\u78ba\u7387\u6bcd\u95a2\u6570<\/a>\uff1a\u96e2\u6563\u578b\u78ba\u7387\u5909\u6570\u306b\u3064\u3044\u3066\\(k\\)\u6b21\u306e\u968e\u4e57\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u6c42\u3081\u308b\u305f\u3081\u306e\u95a2\u6570\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/mgf\">\u7a4d\u7387\u6bcd\u95a2\u6570<\/a>\uff1a\\(k\\)\u6b21\u306e\u539f\u70b9\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u3092\u6c42\u3081\u308b\u305f\u3081\u306e\u95a2\u6570\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cf\">\u7279\u6027\u95a2\u6570<\/a>\uff1a\u7a4d\u7387\u6bcd\u95a2\u6570\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/cgf\">\u30ad\u30e5\u30e0\u30e9\u30f3\u30c8\u6bcd\u95a2\u6570<\/a>\uff1a\u30ad\u30e5\u30df\u30e5\u30e9\u30f3\u30c8\u3092\u7528\u3044\u3066\u7a4d\u7387\u6bcd\u95a2\u6570\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/gf-relationship\">\u6bcd\u95a2\u6570\u9593\u306e\u95a2\u4fc2\u306e\u307e\u3068\u3081<\/a>\uff1a\u6bcd\u95a2\u6570\u9593\u306e\u95a2\u4fc2\u3092\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u9ad8\u6821\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2605\u2606\u2606\u2606 \u5e73\u5747\u3084\u5206\u6563\u306a\u3069\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u304c\u30e2\u30fc\u30e1\u30f3\u30c8\uff08\u7a4d\u7387\uff09\u3067\u3059\u3002\u30e2\u30fc\u30e1\u30f3\u30c8\u306b\u306f[\u539f\u70b9\u307e\u308f\u308a\u306e\u30e2\u30fc\u30e1\u30f3\u30c8]\u3068[ &#8230; <\/p>\n","protected":false},"author":1,"featured_media":1202,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[76],"tags":[77,92],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/9fc17caf-9cad-4670-b857-eb43ec911ab9.png","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1185"}],"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=1185"}],"version-history":[{"count":20,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1185\/revisions"}],"predecessor-version":[{"id":3110,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1185\/revisions\/3110"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/1202"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=1185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=1185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=1185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}