{"id":220,"date":"2023-08-04T01:16:05","date_gmt":"2023-08-04T01:16:05","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%ad%a6%e7%94%9f%e5%88%86%e5%b8%83\/"},"modified":"2023-08-04T01:16:05","modified_gmt":"2023-08-04T01:16:05","slug":"%e5%ad%a6%e7%94%9f%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%ad%a6%e7%94%9f%e5%88%86%e5%b8%83\/","title":{"rendered":"\u5b66\u751f t \u5206\u5e03"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86 Student t \u5206\u5e03\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u6b64\u5916\uff0c\u8fd8\u663e\u793a\u4e86 Student t \u5206\u5e03\u56fe\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387\u5206\u5e03\u7684\u7279\u5f81\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-t-de-student\"><\/span>\u4ec0\u4e48\u662f\u5b66\u751f\u5206\u5e03\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5b66\u751f t \u5206\u5e03<\/strong>\u662f\u7edf\u8ba1\u5b66\u4e2d\u5e7f\u6cdb\u4f7f\u7528\u7684\u6982\u7387\u5206\u5e03\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5b66\u751f t \u5206\u5e03\u5728\u5b66\u751f t \u68c0\u9a8c\u4e2d\u7528\u4e8e\u786e\u5b9a\u4e24\u4e2a\u6837\u672c\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u5e76\u5efa\u7acb\u7f6e\u4fe1\u533a\u95f4\u3002<\/p>\n<p> Student t \u5206\u5e03\u662f\u7531\u7edf\u8ba1\u5b66\u5bb6 William Sealy Gosset \u4e8e 1908 \u5e74\u4ee5\u7b14\u540d\u201cStudent\u201d\u5f00\u53d1\u7684\u3002<\/p>\n<p> Student t \u5206\u5e03\u7531\u5176\u81ea\u7531\u5ea6\u6570\u5b9a\u4e49\uff0c\u81ea\u7531\u5ea6\u6570\u662f\u901a\u8fc7\u4ece\u89c2\u6d4b\u603b\u6570\u4e2d\u51cf\u53bb 1 \u4e2a\u5355\u4f4d\u800c\u83b7\u5f97\u7684\u3002\u56e0\u6b64\uff0c\u786e\u5b9a Student t \u5206\u5e03\u81ea\u7531\u5ea6\u7684\u516c\u5f0f\u4e3a<em>\u03bd=n-1<\/em> \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-1c805dc2d6ca050feb70dad99de53402_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\nu=n-1\\\\[2ex]X\\sim t_\\nu\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"74\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-t-de-student\"><\/span>\u5b66\u751f t \u5206\u5e03\u56fe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86 Student t \u5206\u5e03\u7684\u5b9a\u4e49\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u5b83\u7684\u56fe\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u60a8\u53ef\u4ee5\u5728\u4e0b\u9762\u4ee5\u56fe\u5f62\u65b9\u5f0f\u770b\u5230\u5177\u6709\u4e0d\u540c\u81ea\u7531\u5ea6\u7684 Student t \u5206\u5e03\u7684\u51e0\u4e2a\u793a\u4f8b\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-t-des-etudiants.png\" alt=\"\u5b66\u751f t \u5206\u5e03\u56fe\" class=\"wp-image-4266\" width=\"700\" height=\"420\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4ece Student t \u5206\u5e03\u56fe\u4e2d\uff0c\u53ef\u4ee5\u63a8\u5bfc\u51fa\u4ee5\u4e0b\u5c5e\u6027\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">Student t \u5206\u5e03\u4ee5 0 \u4e3a\u4e2d\u5fc3\u5bf9\u79f0\uff0c\u5448\u949f\u5f62\u3002<\/span><\/li>\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">Student&#8217;s t \u5206\u5e03\u6bd4\u6b63\u6001\u5206\u5e03\u66f4\u52a0\u5206\u6563\uff0c\u5373 Student&#8217;s t \u5206\u5e03\u7684\u66f2\u7ebf\u66f4\u5bbd\u3002<\/span><\/li>\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">Student t \u5206\u5e03\u7684\u81ea\u7531\u5ea6\u8d8a\u5927\uff0c\u5176\u79bb\u6563\u5ea6\u8d8a\u4f4e\u3002<\/span><\/li>\n<\/ul>\n<p>\u5728\u4e0a\u56fe\u4e2d\uff0c\u5df2\u6839\u636e\u5b66\u751f t \u5206\u5e03\u7684\u81ea\u7531\u5ea6\u7ed8\u5236\u4e86\u5bc6\u5ea6\u51fd\u6570\u3002\u4f46\u662f\uff0c\u60a8\u53ef\u4ee5\u5728\u4e0b\u9762\u770b\u5230\u5b66\u751f t \u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u51fd\u6570\u5982\u4f55\u53d8\u5316\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-t-etudiante-cumulative.png\" alt=\"\u5b66\u751f\u7d2f\u79ef t \u5206\u5e03\u56fe\" class=\"wp-image-4267\" width=\"700\" height=\"420\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u67e5\u770b\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u5b66\u751ft\u5206\u5e03\u8868\/\">\u5b66\u751f\u5206\u5e03\u8868<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-t-de-student\"><\/span>\u5b66\u751f t \u5206\u5e03\u7684\u7279\u5f81<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5b66\u751f t \u5206\u5e03\u6700\u91cd\u8981\u7684\u7279\u5f81\u5982\u4e0b\u6240\u793a\u3002<\/p>\n<ul>\n<li> Student t \u5206\u5e03\u7684\u57df\u7531\u5b9e\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-fd8ca9914bdf447012a1a16f7950ce95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (-\\infty, +\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u5177\u6709\u591a\u4e2a\u81ea\u7531\u5ea6\u7684 Student t \u5206\u5e03\uff0c\u5206\u5e03\u7684\u5747\u503c\u7b49\u4e8e 0\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-d4fed5eadcaa1162752aeedb7f8a0906_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim t_\\nu\\\\[2ex] E[X]=0 \\qquad \\text{para }\\nu>1\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;55&#8243; width=&#8221;190&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u5b66\u751f t \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-bfdcbc8a5f071a61e091b0ef6f686a16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim t_\\nu\\\\[2ex] Var(X)=\\cfrac{\\nu}{\\nu-2} \\qquad \\text{para }\\nu>2\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;75&#8243; width=&#8221;245&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u65e0\u8bba\u81ea\u7531\u5ea6\u6709\u591a\u5c11\uff0cStudent t \u5206\u5e03\u7684\u4e2d\u4f4d\u6570\u548c\u4f17\u6570\u59cb\u7ec8\u4e3a 0\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-8d90790fce0c987648c0b30216c82214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Me=0\\\\[2ex]Mo=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"60\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Student t \u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\u7531\u4ee5\u4e0b\u516c\u5f0f\u5b9a\u4e49\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-8c0f1e97a8e407e8b9e2b00ba93aee0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{\\Gamma((\\nu+1)\/2)} {\\sqrt{\\nu\\pi}\\,\\Gamma(\\nu\/2)} (1+x^2\/\\nu)^{-(\\nu+1)\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"339\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Student t \u5206\u5e03\u7684\u7d2f\u79ef\u6982\u7387\u5206\u5e03\u51fd\u6570\u7531\u4ee5\u4e0b\u516c\u5f0f\u5b9a\u4e49\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-da1e3bdf2d87c3a7dcc89c236958dcec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{1}{2} + x \\Gamma \\left( \\frac{\\nu+1}{2} \\right) \\cdot\\frac{\\,_2F_1 \\left ( \\frac{1}{2},\\frac{\\nu+1}{2};\\frac{3}{2};-\\frac{x^2}{\\nu} \\right)}{\\sqrt{\\pi\\nu}\\,\\Gamma \\left(\\frac{\\nu}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"402\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5bf9\u4e8e\u81ea\u7531\u5ea6\u5927\u4e8e 3 \u7684 Student t \u5206\u5e03\uff0c\u4e0d\u5bf9\u79f0\u7cfb\u6570\u4e3a\u96f6\uff0c\u56e0\u4e3a\u5b83\u662f\u5bf9\u79f0\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-6fea0ec5e37ef4db61fb44d6f5eba6fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=0\\qquad \\text{para }\\nu>3&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;17&#8243; width=&#8221;164&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c Student t \u5206\u5e03\u7684\u81ea\u7531\u5ea6\u5927\u4e8e 4\uff0c\u5219\u53ef\u4ee5\u901a\u8fc7\u5c06 6 \u9664\u4ee5\u81ea\u7531\u5ea6\u51cf 4 \u6765\u8ba1\u7b97\u5cf0\u5ea6\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-0335e705ad289732dd1be59dc8388dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\cfrac{6}{\\nu-4}\\qquad \\text{para }\\nu>4&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;38&#8243; width=&#8221;198&#8243; style=&#8221;vertical-align: -12px;&#8221;><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-distribucion-t-de-student\"><\/span>\u5b66\u751f t \u5206\u5e03\u7684\u5e94\u7528<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5b66\u751f t \u5206\u5e03\u662f\u7edf\u8ba1\u5b66\u4e2d\u5e7f\u6cdb\u4f7f\u7528\u7684\u6982\u7387\u5206\u5e03\u3002\u4e8b\u5b9e\u4e0a\uff0c\u751a\u81f3\u8fd8\u6709\u5b66\u751f t \u68c0\u9a8c\uff0c\u7528\u4e8e\u68c0\u9a8c\u5047\u8bbe\u548c\u7f6e\u4fe1\u533a\u95f4\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5b66\u751f t \u5206\u5e03\u4f7f\u6211\u4eec\u80fd\u591f\u5206\u6790\u4e24\u4e2a\u6837\u672c\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u5b83\u7528\u4e8e\u786e\u5b9a\u4e24\u4e2a\u6837\u672c\u662f\u5426\u5177\u6709\u663e\u7740\u4e0d\u540c\u7684\u5747\u503c\u3002\u540c\u6837\uff0cStudent&#8217;s t \u68c0\u9a8c\u7528\u4e8e\u786e\u5b9a\u7ebf\u6027\u56de\u5f52\u5206\u6790\u83b7\u5f97\u7684\u76f4\u7ebf\u662f\u5426\u6709\u659c\u7387\u3002<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0cStudent t \u5206\u5e03\u7684\u5e94\u7528\u4f9d\u8d56\u4e8e\u5bf9\u7406\u8bba\u4e0a\u9075\u5faa\u6b63\u6001\u5206\u5e03\u7684\u6570\u636e\u96c6\u7684\u5206\u6790\uff0c\u4f46\u89c2\u5bdf\u603b\u6570\u592a\u5c0f\u800c\u65e0\u6cd5\u4f7f\u7528\u8fd9\u79cd\u7c7b\u578b\u7684\u5206\u5e03\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86 Student t \u5206\u5e03\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u6b64\u5916\uff0c\u8fd8\u663e\u793a\u4e86 Student t \u5206\u5e03\u56fe\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387 [&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-220","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\/ 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