{"id":225,"date":"2023-08-03T23:58:33","date_gmt":"2023-08-03T23:58:33","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e4%bc%bd%e7%8e%9b%e5%88%86%e5%b8%83\/"},"modified":"2023-08-03T23:58:33","modified_gmt":"2023-08-03T23:58:33","slug":"%e4%bc%bd%e7%8e%9b%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e4%bc%bd%e7%8e%9b%e5%88%86%e5%b8%83\/","title":{"rendered":"\u4f3d\u9a6c\u5206\u5e03"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u4f3d\u739b\u5206\u5e03\u53ca\u5176\u7528\u9014\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u627e\u5230\u4f3d\u9a6c\u5206\u5e03\u7684\u5b9a\u4e49\u3001\u5176\u5c5e\u6027\u53ca\u5176\u56fe\u5f62\u8868\u793a\u5f62\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-gamma\"><\/span>\u4ec0\u4e48\u662f\u4f3d\u9a6c\u5206\u5e03\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4f3d\u9a6c\u5206\u5e03<\/strong>\u662f\u7531\u4e24\u4e2a\u7279\u5f81\u53c2\u6570 \u03b1 \u548c \u03bb \u5b9a\u4e49\u7684\u8fde\u7eed\u6982\u7387\u5206\u5e03\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4f3d\u9a6c\u5206\u5e03\u53d6\u51b3\u4e8e\u5176\u4e24\u4e2a\u53c2\u6570\u7684\u503c\uff1a\u03b1 \u662f\u5f62\u72b6\u53c2\u6570\uff0c\u03bb \u662f\u5c3a\u5ea6\u53c2\u6570\u3002<\/p>\n<p>\u4f3d\u9a6c\u5206\u5e03\u7684\u7b26\u53f7\u662f\u5927\u5199\u5e0c\u814a\u5b57\u6bcd \u0413\u3002\u56e0\u6b64\uff0c\u5982\u679c\u968f\u673a\u53d8\u91cf\u670d\u4ece\u4f3d\u739b\u5206\u5e03\uff0c\u5219\u53ef\u4ee5\u5199\u6210\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1b0ab2e724ffd74455d0907b39f4a598_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\Gamma(\\alpha,\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4f3d\u739b\u5206\u5e03\u8fd8\u53ef\u4ee5\u4f7f\u7528\u5f62\u72b6\u53c2\u6570 k = \u03b1 \u548c\u53cd\u6bd4\u4f8b\u53c2\u6570 \u03b8 = 1\/\u03bb \u8fdb\u884c\u53c2\u6570\u5316\u3002\u5728\u6240\u6709\u60c5\u51b5\u4e0b\uff0c\u5b9a\u4e49\u4f3d\u739b\u5206\u5e03\u7684\u4e24\u4e2a\u53c2\u6570\u90fd\u662f\u6b63\u5b9e\u6570\u3002<\/p>\n<p>\u901a\u5e38\uff0c\u4f3d\u739b\u5206\u5e03\u7528\u4e8e\u5bf9\u53f3\u504f\u6570\u636e\u96c6\u8fdb\u884c\u5efa\u6a21\uff0c\u4ee5\u4fbf\u56fe\u8868\u5de6\u4fa7\u7684\u6570\u636e\u66f4\u52a0\u96c6\u4e2d\u3002\u4f8b\u5982\uff0c\u4f3d\u739b\u5206\u5e03\u7528\u4e8e\u5bf9\u7535\u6c14\u5143\u4ef6\u7684\u53ef\u9760\u6027\u8fdb\u884c\u5efa\u6a21\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-gamma\"><\/span>\u4f3d\u9a6c\u5206\u5e03\u56fe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4f3d\u739b\u5206\u5e03\u7684\u56fe\u5f62\u53d6\u51b3\u4e8e\u5176\u7279\u5f81\u53c2\u6570\u7684\u503c\u3002\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230\u4f3d\u9a6c\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u5982\u4f55\u6839\u636e\u5f62\u72b6\u53c2\u6570\u548c\u5c3a\u5ea6\u53c2\u6570\u800c\u53d8\u5316\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/trace-de-distribution-gamma.png\" alt=\"\u4f3d\u739b\u5206\u5e03\u56fe\" class=\"wp-image-4536\" width=\"648\" height=\"388\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u4e0b\u9762\u7684\u4f3d\u739b\u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u51fd\u6570\u56fe\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-gamma-probabilite-cumulative.png\" alt=\"Gamm \u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u51fd\u6570\u56fe\" class=\"wp-image-4537\" width=\"648\" height=\"388\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-gamma\"><\/span>\u4f3d\u739b\u5206\u5e03\u7684\u7279\u5f81<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u6765\u770b\u770b\u4f3d\u739b\u5206\u5e03\u7684\u7279\u70b9\u662f\u4ec0\u4e48\u3002<\/p>\n<ul>\n<li>\u4f3d\u9a6c\u5206\u5e03\u56fe\u5b8c\u5168\u7531\u5176\u4e24\u4e2a\u7279\u5f81\u53c2\u6570\u5b9a\u4e49\uff1a\u03b1 \u662f\u5f62\u72b6\u53c2\u6570\uff0c\u03bb \u662f\u5c3a\u5ea6\u53c2\u6570\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9640d41832cbcef7d0a7791c55ace57e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha , \\lambda >0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;16&#8243; width=&#8221;62&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u4f3d\u739b\u5206\u5e03\u7684\u57df\u4ec5\u7531\u6b63\u6570\u7ec4\u6210\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f543506f97e1f9c5a56ccc4566a3febf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (0,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4f3d\u739b\u5206\u5e03\u7684\u5747\u503c\u7b49\u4e8e\u5f62\u72b6\u53c2\u6570\u548c\u5c3a\u5ea6\u53c2\u6570\u4e4b\u95f4\u7684\u6bd4\u7387\uff0c\u5373\u03b1\/\u03bb\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-326373413d0fe34ef96959dabe9c5cbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{\\alpha}{\\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"78\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4f3d\u739b\u5206\u5e03\u7684\u65b9\u5dee\u7b49\u4e8e\u5f62\u72b6\u53c2\u6570\u9664\u4ee5\u5c3a\u5ea6\u53c2\u6570\u7684\u5e73\u65b9\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-693a549de92268ac21add32944199974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{\\alpha}{\\lambda^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"107\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u5c0f\u4e8e 1 \u7684 \u03b1 \u503c\uff0c\u4f17\u6570\u4e3a 0\u3002\u4f46\u5982\u679c \u03b1 \u7b49\u4e8e\u6216\u5927\u4e8e 1\uff0c\u5219\u4f3d\u9a6c\u5206\u5e03\u7684\u4f17\u6570\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c9e2762af62f9c38870902ec0284ee07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Mo=0 \\qquad \\text{para } \\alpha<1\\\\[2ex]Mo=\\cfrac{\\alpha-1}{\\lambda} \\qquad \\text{para } \\alpha\\geq1\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"75\" width=\"214\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4f3d\u739b\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u7684\u516c\u5f0f\u4e3a\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-41689ffee11808eab10064a7f3a77693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{\\lambda(\\lambda x)^{\\alpha-1}e^{-\\lambda x}}{\\Gamma(\\alpha)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"168\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5176\u4e2d \u0393 \u4e3a\u4f3d\u739b\u51fd\u6570\uff0c\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6e244faebd1174cb6a56e4254bdaaec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\Gamma(\\alpha)=\\int_0^\\infty t^{\\alpha-1}e^{-t}dt\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"169\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li>\u7531\u4f3d\u739b\u5206\u5e03\u5b9a\u4e49\u7684\u968f\u673a\u53d8\u91cf\u7684\u7d2f\u79ef\u5206\u5e03\u7684\u516c\u5f0f\u5982\u4e0b\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6bc3247a247daec5048c409319dc3943_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle F(x)=\\int_0^x\\frac{\\lambda(\\lambda y)^{\\alpha-1}e^{-\\lambda y}}{\\Gamma(\\alpha)}\\;dy\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"224\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c\u5f62\u72b6\u53c2\u6570 \u03b1 \u7b49\u4e8e 1\uff0c\u5219\u4f3d\u739b\u5206\u5e03\u76f8\u5f53\u4e8e\u5177\u6709\u76f8\u540c\u5c3a\u5ea6\u53c2\u6570 \u03bb \u7684\u6307\u6570\u5206\u5e03\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-60ed376f92f0db2c22e19f85bb76f828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\Gamma(1,\\lambda) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim \\text{Exp}(\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"321\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5f53\u5c3a\u5ea6\u53c2\u6570 \u03bb \u4e3a\u5e73\u5747\u503c\u65f6\uff0c\u4f3d\u9a6c\u5206\u5e03\u662f<a href=\"https:\/\/statorials.org\/cn\/\u5361\u65b9\u5206\u5e03\/\">\u5361\u65b9\u5206\u5e03<\/a>\u7684\u7279\u4f8b\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-efb733464c432d7d1b22ed7e5c534979_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X\\sim \\Gamma\\left(\\frac{n}{2},\\frac{1}{2}\\right) \\text{con } n\\in \\mathbb{N}\\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim \\chi_n^2\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"389\" style=\"vertical-align: -17px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u4f3d\u739b\u5206\u5e03\u53ca\u5176\u7528\u9014\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u627e\u5230\u4f3d\u9a6c\u5206\u5e03\u7684\u5b9a\u4e49\u3001\u5176\u5c5e\u6027\u53ca\u5176\u56fe\u5f62\u8868\u793a\u5f62\u5f0f\u3002 \u4ec0\u4e48\u662f\u4f3d\u9a6c\u5206\u5e03\uff1f \u4f3d [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-225","post","type-post","status-publish","format-standard","hentry","category-12"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u4f3d\u739b\u5206\u5e03<\/title>\n<meta name=\"description\" content=\"\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u4f3d\u739b\u5206\u5e03\u3001\u5b83\u7684\u7528\u9014\u3001\u5b83\u7684\u56fe\u5f62\u4ee5\u53ca\u4f3d\u739b\u5206\u5e03\u7684\u7279\u5f81\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/cn\/\u4f3d\u739b\u5206\u5e03\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" 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