{"id":228,"date":"2023-08-03T22:40:38","date_gmt":"2023-08-03T22:40:38","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%a8%81%e5%b8%83%e5%b0%94%e5%88%86%e5%b8%83\/"},"modified":"2023-08-03T22:40:38","modified_gmt":"2023-08-03T22:40:38","slug":"%e5%a8%81%e5%b8%83%e5%b0%94%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%a8%81%e5%b8%83%e5%b0%94%e5%88%86%e5%b8%83\/","title":{"rendered":"\u5a01\u5e03\u5c14\u5206\u5e03"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u5a01\u5e03\u5c14\u5206\u5e03\u53ca\u5176\u7528\u9014\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u56fe\u5f62\u8868\u793a\u4ee5\u53ca\u8fd9\u79cd\u7c7b\u578b\u7684\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-de-weibull\"><\/span>\u4ec0\u4e48\u662f\u5a01\u5e03\u5c14\u5206\u5e03\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5a01\u5e03\u5c14\u5206\u5e03<\/strong>\u662f\u7531\u4e24\u4e2a\u7279\u5f81\u53c2\u6570\u5b9a\u4e49\u7684\u8fde\u7eed\u6982\u7387\u5206\u5e03\uff1a\u5f62\u72b6\u53c2\u6570 \u03b1 \u548c\u5c3a\u5ea6\u53c2\u6570 \u03bb\u3002<\/p>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5a01\u5e03\u5c14\u5206\u5e03\u4e3b\u8981\u7528\u4e8e\u751f\u5b58\u5206\u6790\u3002\u540c\u6837\uff0c\u5a01\u5e03\u5c14\u5206\u5e03\u5728\u4e0d\u540c\u9886\u57df\u6709\u8bb8\u591a\u5e94\u7528\u3002\u6211\u4eec\u5c06\u5728\u4e0b\u9762\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528\u5a01\u5e03\u5c14\u5206\u5e03\u3002<\/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-14be9904756b25df209befbae173e29e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim\\text{Weibull}(\\alpha,\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u636e\u4f5c\u8005\u4ecb\u7ecd\uff0c\u5a01\u5e03\u5c14\u5206\u5e03\u4e5f\u53ef\u4ee5\u7528\u4e09\u4e2a\u53c2\u6570\u8fdb\u884c\u53c2\u6570\u5316\u3002\u7136\u540e\uff0c\u6dfb\u52a0\u7b2c\u4e09\u4e2a\u53c2\u6570\uff0c\u79f0\u4e3a\u9608\u503c\uff0c\u8be5\u53c2\u6570\u6307\u793a\u5206\u5e03\u56fe\u5f00\u59cb\u7684\u6a2a\u5750\u6807\u3002<\/p>\n<p>\u5a01\u5e03\u5c14\u5206\u5e03\u4ee5\u745e\u5178\u4eba Waloddi Weibull \u7684\u540d\u5b57\u547d\u540d\uff0c\u4ed6\u5728 1951 \u5e74\u5bf9\u5176\u8fdb\u884c\u4e86\u8be6\u7ec6\u63cf\u8ff0\u3002\u7136\u800c\uff0c\u5a01\u5e03\u5c14\u5206\u5e03\u662f\u7531 Maurice Fr\u00e9chet \u4e8e 1927 \u5e74\u53d1\u73b0\u7684\uff0c\u5e76\u7531 Rosin \u548c Rammler \u4e8e 1933 \u5e74\u9996\u6b21\u5e94\u7528\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-de-weibull\"><\/span>\u7ed8\u5236\u5a01\u5e03\u5c14\u5206\u5e03\u56fe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u5c31\u4f1a\u770b\u5230\u5b83\u7684\u56fe\u5f62\u8868\u793a\u5982\u4f55\u6839\u636e\u5176\u53c2\u6570\u503c\u800c\u53d8\u5316\u3002<\/p>\n<p>\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230\u51e0\u4e2a\u793a\u4f8b\uff0c\u8bf4\u660e\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u56fe\u5982\u4f55\u6839\u636e\u5f62\u72b6\u53c2\u6570\u548c\u5c3a\u5ea6\u53c2\u6570\u7684\u503c\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\/graphique-de-distribution-de-weibull.png\" alt=\"\u5a01\u5e03\u5c14\u5206\u5e03\u56fe\" class=\"wp-image-4592\" width=\"613\" height=\"403\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u5f53\u4f7f\u7528\u5a01\u5e03\u5c14\u5206\u5e03\u5bf9\u7cfb\u7edf\u6545\u969c\u7387\u968f\u65f6\u95f4\u7684\u53d8\u5316\u8fdb\u884c\u5efa\u6a21\u65f6\uff0c\u5f62\u72b6\u53c2\u6570 \u03b1 \u7684\u503c\u542b\u4e49\u5982\u4e0b\uff1a<\/p>\n<ul>\n<li> \u03b1&lt;1\uff1a\u6545\u969c\u7387\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\u800c\u964d\u4f4e\u3002<\/li>\n<li> \u03b1=1\uff1a\u6545\u969c\u7387\u968f\u65f6\u95f4\u4fdd\u6301\u6052\u5b9a\u3002<\/li>\n<li> \u03b1&gt;1\uff1a\u6545\u969c\u7387\u968f\u65f6\u95f4\u589e\u52a0\u3002<\/li>\n<\/ul>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u4e0b\u56fe\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u6839\u636e\u5176\u7279\u5f81\u503c\u7ed8\u5236\u7684\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u51fd\u6570\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-de-probabilite-cumulative-weibull.png\" alt=\"\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\" class=\"wp-image-4593\" width=\"613\" height=\"403\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-de-weibull\"><\/span>\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u7279\u5f81<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5a01\u5e03\u5c14\u5206\u5e03\u5177\u6709\u4ee5\u4e0b\u7279\u70b9\uff1a<\/p>\n<ul>\n<li>\u5a01\u5e03\u5c14\u5206\u5e03\u6709\u4e24\u4e2a\u5b9a\u4e49\u5176\u56fe\u5f62\u7684\u7279\u5f81\u53c2\u6570\uff1a\u5f62\u72b6\u53c2\u6570 \u03b1 \u548c\u5c3a\u5ea6\u53c2\u6570 \u03bb\u3002\u4e24\u4e2a\u53c2\u6570\u90fd\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-c8794febbd607514546841a325490654_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\alpha >0\\\\[2ex]\\lambda >0\\\\[2ex]\\text{Weibull}(\\alpha,\\lambda)\\end{array}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;92&#8243; width=&#8221;101&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u5a01\u5e03\u5c14\u5206\u5e03\u4ec5\u63a5\u53d7\u6b63\u6a2a\u5750\u6807\u503c\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>\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u5e73\u5747\u503c\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-58afc005f8ebaae21871a37b7cfdd7bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E[X]=\\frac{1}{\\lambda}\\;\\Gamma\\left(1+\\frac{1}{\\alpha}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"166\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li>\u53e6\u4e00\u65b9\u9762\uff0c\u6c42\u5a01\u5e03\u5c14\u5206\u5e03\u65b9\u5dee\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-d8f2f9c09c6b73fa3e123f115e9d9530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Var(X)=\\frac{1}{\\lambda^2}\\left[\\Gamma\\left(1+\\frac{2}{\\alpha}\\right)-\\Gamma^2\\left(1+\\frac{1}{\\alpha}\\right)\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"326\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li>\u670d\u4ece \u03b1&gt;1 \u7684\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u7684\u4f17\u6570\u53ef\u4ee5\u7531\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u786e\u5b9a\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-6c5647358e9616b85e1a3291e54f4174_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Mo=\\frac{1}{\\lambda}\\left(\\frac{\\alpha-1}{\\alpha} \\right)^{\\frac{1}{\\alpha}} \\quad \\text{para } \\alpha>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;50&#8243; width=&#8221;257&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u5a01\u5e03\u5c14\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-68b68faeb4d3fb2655c6d26eb4225303_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\lambda\\alpha(\\lambda x)^{\\alpha-1}e^{-(\\lambda x)^\\alpha}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"232\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u7c7b\u4f3c\u5730\uff0c\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\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-d57cc3d761634b9239dcbbbfdd92638d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=1- e^{-(\\lambda x)^\\alpha}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"180\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u4e0d\u5bf9\u79f0\u7cfb\u6570\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-77648f1d0bee1b11d4ecd04234074ef7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\frac{\\displaystyle\\Gamma\\left(1+\\frac{3}{\\alpha}\\right)\\frac{|}{\\lambda^3}-3\\mu\\sigma^2-\\mu^3}{\\sigma^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"250\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li>\u6700\u540e\uff0c\u53ef\u4ee5\u786e\u5b9a\u5a01\u5e03\u5c14\u5206\u5e03\u5cf0\u5ea6\u7cfb\u6570\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-bd1311dcff7b84f959830e21a067a85a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\frac{\\displaystyle\\frac{1}{\\lambda^4}\\Gamma \\left(1+\\frac{4}{\\alpha}\\right)-4\\gamma_{1}\\sigma^3\\mu-6\\mu^2\\sigma^2-\\mu^4}{\\sigma^4} \" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"332\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/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-9b8fb16186e6b05715bbb4dba92c740e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Gamma_i=\\Gamma\\left(1+\\frac{i}{\\alpha}\\right).\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"121\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-distribucion-de-weibull\"><\/span>\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u5e94\u7528<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5a01\u5e03\u5c14\u5206\u5e03\u6709\u8bb8\u591a\u5e94\u7528\uff0c\u5305\u62ec\uff1a<\/p>\n<ul>\n<li>\u5728\u5e94\u7528\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5a01\u5e03\u5c14\u5206\u5e03\u7528\u4e8e\u751f\u5b58\u5206\u6790\u3002<\/li>\n<li>\u5728\u5de5\u7a0b\u4e2d\uff0c\u5a01\u5e03\u5c14\u5206\u5e03\u7528\u4e8e\u5bf9\u4e0e\u5236\u9020\u65f6\u95f4\u76f8\u5173\u7684\u51fd\u6570\u8fdb\u884c\u5efa\u6a21\u3002<\/li>\n<li>\u5728\u96f7\u8fbe\u7cfb\u7edf\u4e2d\uff0c\u6a21\u62df\u63a5\u6536\u4fe1\u53f7\u7684\u8272\u6563\u3002<\/li>\n<li>\u5728\u4fdd\u9669\u9886\u57df\uff0c\u5bf9\u7d22\u8d54\u8303\u56f4\u8fdb\u884c\u5efa\u6a21\u3002<\/li>\n<li>\u4f8b\u5982\uff0c\u5728\u6c14\u8c61\u5b66\u4e2d\uff0c\u5bf9\u4e0d\u540c\u98ce\u901f\u7684\u9891\u7387\u8fdb\u884c\u5efa\u6a21\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u5a01\u5e03\u5c14\u5206\u5e03\u53ca\u5176\u7528\u9014\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u56fe\u5f62\u8868\u793a\u4ee5\u53ca\u8fd9\u79cd\u7c7b\u578b\u7684\u6982\u7387\u5206\u5e03\u7684\u5c5e\u6027\u3002 \u4ec0\u4e48 [&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-228","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\u5a01\u5e03\u5c14\u5206\u5e03<\/title>\n<meta name=\"description\" content=\"\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u5a01\u5e03\u5c14\u5206\u5e03\u3001\u5b83\u7684\u56fe\u5f62\u3001\u5a01\u5e03\u5c14\u5206\u5e03\u7684\u7279\u5f81\u53ca\u5176\u5e94\u7528\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\/\u5a01\u5e03\u5c14\u5206\u5e03\/\" \/>\n<meta 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