{"id":219,"date":"2023-08-04T00:57:07","date_gmt":"2023-08-04T00:57:07","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-f-da-snedecor\/"},"modified":"2023-08-04T00:57:07","modified_gmt":"2023-08-04T00:57:07","slug":"distribuicao-f-da-snedecor","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-f-da-snedecor\/","title":{"rendered":"Snedecor f distribui\u00e7\u00e3o"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o Snedecor F e para que \u00e9 utilizada. Al\u00e9m disso, voc\u00ea poder\u00e1 ver o gr\u00e1fico de distribui\u00e7\u00e3o do Snedecor F e quais s\u00e3o suas propriedades estat\u00edsticas. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-f-de-snedecor\"><\/span> Qual \u00e9 a distribui\u00e7\u00e3o Snedecor F?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o F de Snedecor<\/strong> , tamb\u00e9m chamada <strong>de distribui\u00e7\u00e3o F de Fisher-Snedecor<\/strong> ou simplesmente <strong>distribui\u00e7\u00e3o F<\/strong> , \u00e9 uma distribui\u00e7\u00e3o de probabilidade cont\u00ednua usada em infer\u00eancia estat\u00edstica, particularmente em an\u00e1lise de vari\u00e2ncia.<\/p>\n<p> Uma das propriedades da distribui\u00e7\u00e3o Snedecor F \u00e9 que ela \u00e9 definida pelo valor de dois par\u00e2metros reais, <em>m<\/em> e <em>n<\/em> , que indicam seus graus de liberdade. Assim, o s\u00edmbolo para a distribui\u00e7\u00e3o Snedecor F \u00e9 <em>F <sub>m,n<\/sub><\/em> , onde <em>m<\/em> e <em>n<\/em> s\u00e3o os par\u00e2metros que definem a distribui\u00e7\u00e3o.<\/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-b6126a79c671267450b6523ca16b4a92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F_{m,n}\\qquad m,n>0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;18&#8243; width=&#8221;139&#8243; style=&#8221;vertical-align: -6px;&#8221;><\/p>\n<\/p>\n<p> Matematicamente, a distribui\u00e7\u00e3o Snedecor F \u00e9 igual ao quociente entre uma distribui\u00e7\u00e3o qui-quadrado e seus graus de liberdade dividido pelo quociente entre outra distribui\u00e7\u00e3o qui-quadrado e seus graus de liberdade. Assim, a f\u00f3rmula que define a distribui\u00e7\u00e3o Snedecor F \u00e9 a seguinte: <\/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-d407869e61ca4357ffbcb40df3bd83ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{c} X\\sim \\chi_m^2\\\\[2ex] Y\\sim \\chi_n^2\\end{array}\\right\\}\\color{orange}\\bm{\\longrightarrow}\\color{black}\\ F_{m,n}= \\cfrac{X\/m}{Y\/n}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"322\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-qui-quadrado\/\">Qual \u00e9 a distribui\u00e7\u00e3o qui-quadrado?<\/a><\/div>\n<p> A distribui\u00e7\u00e3o Fisher-Snedecor F deve seu nome ao estat\u00edstico ingl\u00eas Ronald Fisher e ao estat\u00edstico americano George Snedecor.<\/p>\n<p> Em estat\u00edstica, a distribui\u00e7\u00e3o Fisher-Snedecor F tem diferentes aplica\u00e7\u00f5es. Por exemplo, a distribui\u00e7\u00e3o Fisher-Snedecor F \u00e9 usada para comparar diferentes modelos de regress\u00e3o linear, e esta distribui\u00e7\u00e3o de probabilidade \u00e9 usada na an\u00e1lise de vari\u00e2ncia (ANOVA). <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-f-de-snedecor\"><\/span> Diagrama de distribui\u00e7\u00e3o Snedecor F<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos a defini\u00e7\u00e3o da distribui\u00e7\u00e3o Snedecor F, o gr\u00e1fico da sua fun\u00e7\u00e3o densidade e o gr\u00e1fico da sua probabilidade cumulativa s\u00e3o mostrados abaixo.<\/p>\n<p> No gr\u00e1fico abaixo voc\u00ea pode ver v\u00e1rios exemplos de distribui\u00e7\u00f5es Snedecor F com diferentes graus de liberdade. <\/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-f-de-snedecor.png\" alt=\"Gr\u00e1fico de distribui\u00e7\u00e3o Snedecor F\" class=\"wp-image-4375\" width=\"700\" height=\"419\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Por outro lado, no gr\u00e1fico abaixo voc\u00ea pode ver como o gr\u00e1fico da fun\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o Snedecor F varia em fun\u00e7\u00e3o de seus valores caracter\u00edsticos. <\/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-f-de-snedecor-probabilite-cumulative.png\" alt=\"probabilidade cumulativa da distribui\u00e7\u00e3o Snedecor F\" class=\"wp-image-4377\" width=\"700\" height=\"419\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-f-de-snedecor\"><\/span> Caracter\u00edsticas da distribui\u00e7\u00e3o Snedecor F<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Finalmente, esta se\u00e7\u00e3o apresenta as caracter\u00edsticas mais importantes da distribui\u00e7\u00e3o Snedecor F.<\/p>\n<ul>\n<li> Os graus de liberdade da distribui\u00e7\u00e3o Snedecor F, <em>m<\/em> e <em>n<\/em> , s\u00e3o dois par\u00e2metros que definem a forma da distribui\u00e7\u00e3o. Esses valores caracter\u00edsticos da distribui\u00e7\u00e3o Snedecor F s\u00e3o n\u00fameros inteiros positivos.<\/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-043df156b055e7088fa83fe733825632_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}m,n \\in \\mathbb{Z}\\\\[2ex] m,n>0\\end{array}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;54&#8243; width=&#8221;68&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> O dom\u00ednio da distribui\u00e7\u00e3o Snedecor F consiste em todos os n\u00fameros reais maiores ou iguais a zero.<\/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-0b8fb6676086841f8e7454004bfb39da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in [0,+\\infty) \" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Para valores de <em>n<\/em> maiores que 2, a m\u00e9dia da distribui\u00e7\u00e3o Snedecor F \u00e9 igual a <em>n<\/em> na subtra\u00e7\u00e3o de <em>n<\/em> menos 2.<\/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-5861b8fbc6e7aef8cac0eb21cad00c9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim F_{m,n}\\\\[2ex] E[X]=\\cfrac{n}{n-2} \\qquad \\text{para }n>2\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;75&#8243; width=&#8221;225&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Quando o par\u00e2metro <em>n<\/em> \u00e9 maior que 2, a vari\u00e2ncia da distribui\u00e7\u00e3o Snedecor F pode ser calculada aplicando a seguinte f\u00f3rmula:<\/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-9a284413da889eec7ac2e9a95e255169_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim F_{m,n}\\\\[2ex] Var(X)=\\cfrac{2n^2\\cdot (m+n-2)}{m\\cdot (n-2)^2\\cdot (n-4)} \\qquad \\text{para }n>4\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;80&#8243; width=&#8221;366&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Se o par\u00e2metro <em>m<\/em> for maior que 2, a moda da distribui\u00e7\u00e3o Snedecor F pode ser calculada com a seguinte express\u00e3o:<\/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-45d29450e457b8fa07c41227c7b407e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=\\cfrac{m-2}{m}\\cdot \\cfrac{n}{n+2}\\qquad \\text{para }m>2&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;40&#8243; width=&#8221;278&#8243; style=&#8221;vertical-align: -14px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> A f\u00f3rmula para a fun\u00e7\u00e3o densidade da distribui\u00e7\u00e3o Snedecor F \u00e9 a seguinte:<\/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-06871a7baaf462b75f545a02eac7dd11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{\\Gamma\\left(\\frac{m+n}{2}\\right)}{\\Gamma\\left(\\frac{m}{2}\\right)\\Gamma\\left(\\frac{n}{2}\\right)}\\left(\\frac{m}{n}\\right)^{\\frac{m}{2}}\\cdot\\frac{x^{\\frac{m-2}{2}}}{\\left(1+\\frac{mx}{n}\\right)^{\\frac{m+n}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"370\" style=\"vertical-align: -26px;\"><\/p>\n<\/p>\n<ul>\n<li> Se uma vari\u00e1vel segue uma distribui\u00e7\u00e3o Snedecor F com graus de liberdade <em>m<\/em> e <em>n<\/em> , ent\u00e3o o inverso da referida vari\u00e1vel segue uma distribui\u00e7\u00e3o Snedecor F com os mesmos graus de liberdade mas alterando a ordem dos seus valores.<\/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-33587ac8fb53a8c4360dfa7f54da2792_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim F_{m,n} \\ \\color{orange}\\bm{\\longrightarrow}\\color{\\black} \\ X^{-1}\\sim F_{n,m}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"264\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<ul>\n<li> A distribui\u00e7\u00e3o Student tem a seguinte rela\u00e7\u00e3o com a distribui\u00e7\u00e3o Snedecor F: <\/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-3efae8413f4588d5f30ae36f2b96a4d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim t_n \\ \\color{orange}\\bm{\\longrightarrow}\\color{\\black} \\ X^2\\sim F_{1,n}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"228\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\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>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-de-alunos\/\">Qual \u00e9 a distribui\u00e7\u00e3o t de Student?<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o Snedecor F e para que \u00e9 utilizada. Al\u00e9m disso, voc\u00ea poder\u00e1 ver o gr\u00e1fico de distribui\u00e7\u00e3o do Snedecor F e quais s\u00e3o suas propriedades estat\u00edsticas. Qual \u00e9 a distribui\u00e7\u00e3o Snedecor F? A distribui\u00e7\u00e3o F de Snedecor , tamb\u00e9m chamada de distribui\u00e7\u00e3o F de Fisher-Snedecor ou simplesmente distribui\u00e7\u00e3o [&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-219","post","type-post","status-publish","format-standard","hentry","category-probabilidade"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Distribui\u00e7\u00e3o F da Snedecor<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o Snedecor F, para que serve, suas caracter\u00edsticas e o gr\u00e1fico de distribui\u00e7\u00e3o Snedecor F.\" \/>\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\/pt\/distribuicao-f-da-snedecor\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Distribui\u00e7\u00e3o F da Snedecor\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o Snedecor F, para que serve, suas caracter\u00edsticas e o gr\u00e1fico de distribui\u00e7\u00e3o Snedecor F.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-f-da-snedecor\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-04T00:57:07+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b6126a79c671267450b6523ca16b4a92_l3.png\" \/>\n<meta name=\"author\" content=\"Dr. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-f-da-snedecor\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-f-da-snedecor\/\",\"name\":\"\u25b7 Distribui\u00e7\u00e3o F da Snedecor\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-04T00:57:07+00:00\",\"dateModified\":\"2023-08-04T00:57:07+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o Snedecor F, para que serve, suas caracter\u00edsticas e o gr\u00e1fico de distribui\u00e7\u00e3o Snedecor F.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-f-da-snedecor\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-f-da-snedecor\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-f-da-snedecor\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Snedecor f distribui\u00e7\u00e3o\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. 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