{"id":229,"date":"2023-08-03T22:21:12","date_gmt":"2023-08-03T22:21:12","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%af%b9%e6%95%b0%e6%ad%a3%e6%80%81%e5%88%86%e5%b8%83\/"},"modified":"2023-08-03T22:21:12","modified_gmt":"2023-08-03T22:21:12","slug":"%e5%af%b9%e6%95%b0%e6%ad%a3%e6%80%81%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%af%b9%e6%95%b0%e6%ad%a3%e6%80%81%e5%88%86%e5%b8%83\/","title":{"rendered":"\u5bf9\u6570\u6b63\u6001\u5206\u5e03"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u5c5e\u6027\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387\u5206\u5e03\u7684\u56fe\u5f62\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-lognormal\"><\/span>\u4ec0\u4e48\u662f\u5bf9\u6570\u6b63\u6001\u5206\u5e03\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5bf9\u6570\u6b63\u6001\u5206\u5e03<\/strong>\u6216<strong>\u5bf9\u6570\u6b63\u6001\u5206\u5e03<\/strong>\u662f\u4e00\u79cd\u6982\u7387\u5206\u5e03\uff0c\u5b9a\u4e49\u5176\u5bf9\u6570\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u53d8\u91cf X \u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c\u5219\u6307\u6570\u51fd\u6570 e <sup>x<\/sup>\u670d\u4ece\u5bf9\u6570\u6b63\u6001\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-216d8f120f09a37cd8f797bb3b115a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Lognormal}(\\mu,\\sigma^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u53ea\u80fd\u5728\u53d8\u91cf\u503c\u4e3a\u6b63\u65f6\u4f7f\u7528\uff0c\u56e0\u4e3a\u5bf9\u6570\u662f\u4e00\u79cd\u4ec5\u91c7\u7528\u4e00\u4e2a\u6b63\u53c2\u6570\u7684\u51fd\u6570\u3002<\/p>\n<p>\u5728\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u5728\u7edf\u8ba1\u4e2d\u7684\u4e0d\u540c\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u533a\u5206\u4f7f\u7528\u8be5\u5206\u5e03\u6765\u5206\u6790\u91d1\u878d\u6295\u8d44\u548c\u8fdb\u884c\u53ef\u9760\u6027\u5206\u6790\u3002<\/p>\n<p>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u4e5f\u79f0\u4e3a<strong>Tinaut \u5206\u5e03<\/strong>\uff0c\u6709\u65f6\u4e5f\u5199<strong>\u4e3a\u5bf9\u6570\u6b63\u6001\u5206\u5e03<\/strong>\u6216<strong>\u5bf9\u6570\u6b63\u6001\u5206\u5e03<\/strong>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-lognormal\"><\/span>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u56fe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u5c06\u5728\u672c\u8282\u4e2d\u770b\u5230\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u56fe\u5f62\u8868\u793a\u5982\u4f55\u6839\u636e\u5176\u7b97\u672f\u5e73\u5747\u503c\u548c\u6807\u51c6\u5dee\u7684\u503c\u800c\u53d8\u5316\u3002<\/p>\n<p>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u56fe\u5982\u4e0b\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\/trace-de-distribution-lognormale.png\" alt=\"\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u56fe\" class=\"wp-image-4563\" width=\"675\" height=\"406\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u56fe\u5982\u4e0b\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-de-probabilite-lognormale-cumulative.png\" alt=\"\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u56fe\" class=\"wp-image-4564\" width=\"675\" height=\"404\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-lognormal\"><\/span>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u7279\u5f81<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u5177\u6709\u4ee5\u4e0b\u7279\u5f81\uff1a<\/p>\n<ul>\n<li>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7531\u4e24\u4e2a\u53c2\u6570\u7684\u503c\u5b9a\u4e49\uff0c\u5373\u7b97\u672f\u5e73\u5747\u503c \u03bc \u548c\u65b9\u5dee \u03c3 <sup>2<\/sup> \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-216d8f120f09a37cd8f797bb3b115a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Lognormal}(\\mu,\\sigma^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u57df\u7531\u6b63\u5b9e\u6570\u7ec4\u6210\uff0c\u56e0\u4e3a\u5bf9\u6570\u4e0d\u63a5\u53d7\u8d1f\u503c\u6216\u96f6\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>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u671f\u671b\u7b49\u4e8e\u5e73\u5747\u503c\u52a0\u65b9\u5dee\u4e4b\u548c\u9664\u4ee5 2 \u5f97\u51fa\u7684\u6570\u5b57 e\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-109a1024d530b2993db41f1d7a5a24c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E[X]=e^{\\mu+\\frac{\\sigma^2}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u53e6\u4e00\u65b9\u9762\uff0c\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u65b9\u5dee\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u8868\u8fbe\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-5afc17462bb71082888ab755626b853a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\left(e^{\\sigma^2}-1\\right)\\cdot e^{2\\mu+\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"223\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u4f17\u6570\u76f8\u5f53\u4e8e\u5c06\u6570\u5b57 e \u6c42\u4e3a\u5206\u5e03\u5e73\u5747\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-21b2bd4c45dca8e305c9ee480d961f4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=e^\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"67\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u504f\u5ea6\u7cfb\u6570\u53ef\u4ee5\u901a\u8fc7\u5e94\u7528\u4ee5\u4e0b\u516c\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-2686fd41c4e28d5c396bf494229a63a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\left(e^{\\sigma^2}+2\\right)\\cdot\\sqrt{e^{\\sigma^2}-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"198\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5bf9\u6570\u6b63\u6001\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-25698732745689402d16ea353a072cc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{1}{\\sigma \\cdot x\\cdot \\sqrt{2 \\pi}}\\cdot \\exp\\left(-\\frac{(\\ln x-\\mu)^2}{2\\sigma^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"347\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5bf9\u6570\u6b63\u6001\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-59c2474703bad4805a6a44bd05cf92bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\Phi\\left(\\frac{\\ln x-\\mu}{\\sigma}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"200\" style=\"vertical-align: -17px;\"><\/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-21f36758b04341c7980aa18b13ced720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Phi\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f<a href=\"https:\/\/statorials.org\/cn\/\u6b63\u6001\u6807\u51c6\u5206\u5e03\/\">\u6807\u51c6\u6b63\u6001\u5206\u5e03<\/a>\u7684\u7d2f\u79ef\u6982\u7387\u51fd\u6570\u3002<\/p>\n<ul>\n<li>\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u7b97\u672f\u5e73\u5747\u503c\u5927\u4e8e\u4e2d\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-96e66e8c60e4ce5e235c30258e4ecead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu > Me&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;16&#8243; width=&#8221;61&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5bf9\u6570\u6b63\u6001\u5206\u5e03\u7684\u5c5e\u6027\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387\u5206\u5e03\u7684\u56fe\u5f62\u3002 \u4ec0\u4e48\u662f\u5bf9\u6570\u6b63 [&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-229","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 \u5bf9\u6570\u6b63\u6001\u5206\u5e03<\/title>\n<meta name=\"description\" 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