{"id":216,"date":"2023-08-04T02:39:23","date_gmt":"2023-08-04T02:39:23","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e8%b4%9d%e5%a1%94%e5%88%86%e5%b8%83\/"},"modified":"2023-08-04T02:39:23","modified_gmt":"2023-08-04T02:39:23","slug":"%e8%b4%9d%e5%a1%94%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e8%b4%9d%e5%a1%94%e5%88%86%e5%b8%83\/","title":{"rendered":"\u8d1d\u5854\u5206\u5e03"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f Beta \u53d1\u884c\u7248\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u540c\u6837\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230 beta \u5206\u5e03\u56fe\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387\u5206\u5e03\u7684\u5c5e\u6027\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-beta\"><\/span>\u4ec0\u4e48\u662f\u8d1d\u5854\u5206\u5e03\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>beta \u5206\u5e03<\/strong>\u662f\u5728\u533a\u95f4 (0,1) \u4e0a\u5b9a\u4e49\u7684\u6982\u7387\u5206\u5e03\uff0c\u5e76\u7531\u4e24\u4e2a\u6b63\u53c2\u6570 \u03b1 \u548c \u03b2 \u53c2\u6570\u5316\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u03b2\u5206\u5e03\u7684\u503c\u53d6\u51b3\u4e8e\u53c2\u6570\u03b1\u548c\u03b2\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u03b2\u5206\u5e03\u7684\u4e3b\u8981\u7279\u70b9\u662f\u5176\u5f62\u72b6\u53ef\u4ee5\u7531\u53c2\u6570\u03b1\u548c\u03b2\u63a7\u5236\u3002\u6b64\u5916\uff0c\u03b2 \u5206\u5e03\u7528\u4e8e\u5b9a\u4e49\u503c\u5728 0 \u5230 1 \u4e4b\u95f4\u7684\u968f\u673a\u53d8\u91cf\u3002<\/p>\n<p>\u6709\u51e0\u79cd\u8868\u793a\u6cd5\u8868\u660e\u8fde\u7eed\u968f\u673a\u53d8\u91cf\u53d7 beta \u5206\u5e03\u652f\u914d\uff0c\u6700\u5e38\u89c1\u7684\u662f\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-ee1d0d8a1624a017b8ef9ce8a67c694e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex]X\\sim Beta(\\alpha,\\beta)\\\\[2ex]X\\sim \\beta_{\\alpha,\\beta}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"121\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u03b2 \u5206\u5e03\u7684\u5e94\u7528\u975e\u5e38\u5e7f\u6cdb\u3002\u4f8b\u5982\uff0c\u03b2 \u5206\u5e03\u7528\u4e8e\u7814\u7a76\u4e0d\u540c\u6837\u672c\u4e2d\u767e\u5206\u6bd4\u7684\u53d8\u5316\u3002\u540c\u6837\uff0c\u5728\u9879\u76ee\u7ba1\u7406\u4e2d\uff0c\u03b2\u5206\u5e03\u7528\u4e8e\u8fdb\u884cPert\u5206\u6790\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-beta\"><\/span>\u8d1d\u5854\u5206\u5e03\u56fe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8003\u8651\u5230 beta \u5206\u5e03\u7684\u5b9a\u4e49\uff0cbeta \u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u548c\u6982\u7387\u5206\u5e03\u51fd\u6570\u5982\u4e0b\u56fe\u6240\u793a\u3002<\/p>\n<p>\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230 beta \u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u56fe\u5982\u4f55\u6839\u636e\u53c2\u6570 \u03b1 \u548c \u03b2 \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\/distribution-graphique-beta.png\" alt=\"\u8d1d\u5854\u5206\u5e03\u56fe\" class=\"wp-image-4315\" width=\"621\" height=\"372\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u540c\u6837\uff0c\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230\u57fa\u4e8e\u53c2\u6570 \u03b1 \u548c \u03b2 \u7684 beta \u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u7684\u56fe\u5f62\u8868\u793a\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\/distribution-beta-cumulative.png\" alt=\"\u7d2f\u79ef\u8d1d\u5854\u5206\u5e03\u56fe\" class=\"wp-image-4316\" width=\"621\" height=\"373\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-beta\"><\/span>\u8d1d\u5854\u5206\u5e03\u7684\u7279\u5f81<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3 beta \u5206\u5e03\u6700\u91cd\u8981\u7684\u7279\u5f81\u662f\u4ec0\u4e48\u3002<\/p>\n<ul>\n<li> beta \u5206\u5e03\u7684\u53c2\u6570 \u03b1 \u548c \u03b2 \u662f\u6b63\u5b9e\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-442bebaba847543d6db71cdf0127a4b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\alpha >0\\\\[2ex] \\beta >0\\end{array}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;54&#8243; width=&#8221;44&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> beta\u5206\u5e03\u7684\u57df\u8303\u56f4\u4e3a0\u52301\uff0c\u4e0d\u5305\u62ec\u4e24\u4e2a\u6781\u7aef\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-60f8667881e2c5a08eae2db3c3e04708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> beta \u5206\u5e03\u7684\u5e73\u5747\u503c\u7b49\u4e8e alpha \u9664\u4ee5 alpha \u52a0 beta \u4e4b\u548c\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-4530a8b72211111e8bec79b6388e00a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex] E[X]=\\cfrac{\\alpha}{\\alpha+\\beta}\\end{array} \" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"111\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> beta \u5206\u5e03\u7684\u65b9\u5dee\u53ef\u4ee5\u4f7f\u7528\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-71c6ef40db833722e63c56cd763d6601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex] Var(X)=\\cfrac{\\alpha\\cdot \\beta}{(\\alpha+\\beta+1)\\cdot (\\alpha+\\beta)^2}\\end{array} \" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u5927\u4e8e 1 \u7684 alpha \u548c beta \u503c\uff0c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u8f7b\u677e\u627e\u5230 beta \u5206\u5e03\u6a21\u5f0f\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-472cafc0cf9d1cf782206ddc7c9475d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=\\cfrac{\\alpha-1}{\\alpha+\\beta-2}\\qquad \\alpha,\\beta>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;42&#8243; width=&#8221;225&#8243; style=&#8221;vertical-align: -16px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> beta\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\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-48f1f2a13df23d7c779bc37da4b49368_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{x^{\\alpha-1}(1-x)^{\\beta-1}}{B(\\alpha,\\beta)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"218\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5176\u4e2dB(\u03b1,\u03b2)\u662f\u03b2\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-f4eb1d2659d9993f9d05a35cce63fc14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B(\\alpha,\\beta)=\\int_0^1x^{\\alpha-1}(1-x)^{\\beta-1}dx\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"248\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> Beta \u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u51fd\u6570\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-031b21ea3e2964d3ac4e6f222356d55b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{B(x;\\alpha,\\beta)}{B(\\alpha,\\beta)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"176\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5176\u4e2dB(x;\u03b1,\u03b2)\u662f\u4e0d\u5b8c\u5168beta\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-6c64764f48f86e8f97df5ed1e8d7fbe6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B(x;\\,a,b) = \\int_0^x t^{a-1}\\,(1-t)^{b-1}\\,dt\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"255\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c X \u662f\u7531 beta \u5206\u5e03\u5b9a\u4e49\u7684\u53d8\u91cf\uff0c\u5219 1-X \u662f\u7531 beta \u5206\u5e03\u5b9a\u4e49\u7684\u53d8\u91cf\uff0c\u5176 alpha \u548c beta \u53c2\u6570\u5206\u522b\u662f\u539f\u59cb beta \u5206\u5e03\u7684 beta \u548c alpha \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-c65dd399bb92ffe982784a6c1b6e5b0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim B(\\alpha,\\beta) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ 1-X\\sim B(\\beta,\\alpha)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"361\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c beta \u5206\u5e03\u7684 alpha \u548c beta \u53c2\u6570\u90fd\u7b49\u4e8e 1\uff0c\u5219\u8be5\u5206\u5e03\u76f8\u5f53\u4e8e\u53c2\u6570 0 \u548c 1 \u7684\u5747\u5300\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-10010ad6c6959b44a8ae0fe4361b4034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim B(1,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim U(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"321\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f Beta \u53d1\u884c\u7248\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u540c\u6837\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230 beta \u5206\u5e03\u56fe\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387\u5206\u5e03\u7684\u5c5e\u6027\u3002  [&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-216","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 Beta \u5206\u5e03 - \u6982\u7387\u548c\u7edf\u8ba1<\/title>\n<meta name=\"description\" content=\"\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f Beta \u53d1\u884c\u7248\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u540c\u6837\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230 beta \u5206\u5e03\u56fe\u53ca\u5176\u5c5e\u6027 \u2705\" \/>\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\/\u8d1d\u5854\u5206\u5e03\/\" 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content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u672c\u6770\u660e\u00b7\u5b89\u5fb7\u68ee\u535a\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/cn\/%e8%b4%9d%e5%a1%94%e5%88%86%e5%b8%83\/\",\"url\":\"https:\/\/statorials.org\/cn\/%e8%b4%9d%e5%a1%94%e5%88%86%e5%b8%83\/\",\"name\":\"\u25b7 Beta \u5206\u5e03 - \u6982\u7387\u548c\u7edf\u8ba1\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/cn\/#website\"},\"datePublished\":\"2023-08-04T02:39:23+00:00\",\"dateModified\":\"2023-08-04T02:39:23+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/cn\/#\/schema\/person\/124e4e5b7c9f8dc0f1f95cc8c1db3261\"},\"description\":\"\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f Beta 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