{"id":223,"date":"2023-08-03T23:58:33","date_gmt":"2023-08-03T23:58:33","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-gama\/"},"modified":"2023-08-03T23:58:33","modified_gmt":"2023-08-03T23:58:33","slug":"distribuicao-gama","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-gama\/","title":{"rendered":"Distribui\u00e7\u00e3o gama"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o gama e para que ela \u00e9 usada. Assim, voc\u00ea encontrar\u00e1 a defini\u00e7\u00e3o da distribui\u00e7\u00e3o gama, suas propriedades e como \u00e9 sua representa\u00e7\u00e3o gr\u00e1fica. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-gamma\"><\/span> Qual \u00e9 a distribui\u00e7\u00e3o gama?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o gama<\/strong> \u00e9 uma distribui\u00e7\u00e3o de probabilidade cont\u00ednua definida por dois par\u00e2metros caracter\u00edsticos, \u03b1 e \u03bb. Em outras palavras, a distribui\u00e7\u00e3o gama depende do valor de seus dois par\u00e2metros: \u03b1 \u00e9 o par\u00e2metro de forma e \u03bb \u00e9 o par\u00e2metro de escala.<\/p>\n<p> O s\u00edmbolo da distribui\u00e7\u00e3o gama \u00e9 a letra grega mai\u00fascula \u0393. Portanto, se uma vari\u00e1vel aleat\u00f3ria segue uma distribui\u00e7\u00e3o gama, ela \u00e9 escrita da seguinte forma:<\/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-1b0ab2e724ffd74455d0907b39f4a598_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\Gamma(\\alpha,\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A distribui\u00e7\u00e3o gama tamb\u00e9m pode ser parametrizada usando o par\u00e2metro de forma k = \u03b1 e o par\u00e2metro de escala inversa \u03b8 = 1\/\u03bb. Em todos os casos, os dois par\u00e2metros que definem a distribui\u00e7\u00e3o gama s\u00e3o n\u00fameros reais positivos.<\/p>\n<p> Normalmente, a distribui\u00e7\u00e3o gama \u00e9 usada para modelar conjuntos de dados distorcidos \u00e0 direita, de modo que haja uma maior concentra\u00e7\u00e3o de dados no lado esquerdo do gr\u00e1fico. Por exemplo, a distribui\u00e7\u00e3o gama \u00e9 usada para modelar a confiabilidade de componentes el\u00e9tricos.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-gamma\"><\/span> Diagrama de distribui\u00e7\u00e3o gama<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O gr\u00e1fico da distribui\u00e7\u00e3o gama depende dos valores de seus par\u00e2metros caracter\u00edsticos. Abaixo voc\u00ea pode ver como a fun\u00e7\u00e3o de densidade da distribui\u00e7\u00e3o gama varia dependendo do par\u00e2metro de forma e do par\u00e2metro de escala. <\/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-gamma.png\" alt=\"gr\u00e1fico de distribui\u00e7\u00e3o gama\" class=\"wp-image-4536\" width=\"648\" height=\"388\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Por outro lado, voc\u00ea pode ver o gr\u00e1fico da fun\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o gama abaixo: <\/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-gamma-probabilite-cumulative.png\" alt=\"gr\u00e1fico da fun\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o Gamm\" class=\"wp-image-4537\" width=\"648\" height=\"388\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-gamma\"><\/span> Caracter\u00edsticas da distribui\u00e7\u00e3o gama<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Veremos ent\u00e3o quais s\u00e3o as caracter\u00edsticas da distribui\u00e7\u00e3o gama.<\/p>\n<ul>\n<li> O gr\u00e1fico da distribui\u00e7\u00e3o gama \u00e9 inteiramente definido por seus dois par\u00e2metros caracter\u00edsticos: \u03b1 \u00e9 o par\u00e2metro de forma e \u03bb \u00e9 o par\u00e2metro de escala.<\/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-9640d41832cbcef7d0a7791c55ace57e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha , \\lambda >0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;16&#8243; width=&#8221;62&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> O dom\u00ednio da distribui\u00e7\u00e3o gama \u00e9 composto apenas por n\u00fameros 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-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> A m\u00e9dia da distribui\u00e7\u00e3o gama \u00e9 igual \u00e0 raz\u00e3o entre o par\u00e2metro de forma e o par\u00e2metro de escala, ou seja, \u03b1\/\u03bb.<\/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-326373413d0fe34ef96959dabe9c5cbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{\\alpha}{\\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"78\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> A vari\u00e2ncia da distribui\u00e7\u00e3o gama \u00e9 equivalente ao par\u00e2metro de forma dividido pelo quadrado do par\u00e2metro de escala.<\/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-693a549de92268ac21add32944199974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{\\alpha}{\\lambda^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"107\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Para valores de \u03b1 menores que 1, a moda \u00e9 0. Mas se \u03b1 for igual ou maior que 1, a moda da distribui\u00e7\u00e3o gama pode ser calculada com 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-c9e2762af62f9c38870902ec0284ee07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Mo=0 \\qquad \\text{para } \\alpha<1\\\\[2ex]Mo=\\cfrac{\\alpha-1}{\\lambda} \\qquad \\text{para } \\alpha\\geq1\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"75\" width=\"214\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> A f\u00f3rmula para a fun\u00e7\u00e3o densidade da distribui\u00e7\u00e3o gama \u00e9:<\/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-41689ffee11808eab10064a7f3a77693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{\\lambda(\\lambda x)^{\\alpha-1}e^{-\\lambda x}}{\\Gamma(\\alpha)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"168\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Onde \u0393 \u00e9 a fun\u00e7\u00e3o gama, que \u00e9 definida como:<\/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-6e244faebd1174cb6a56e4254bdaaec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\Gamma(\\alpha)=\\int_0^\\infty t^{\\alpha-1}e^{-t}dt\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"169\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> A f\u00f3rmula para a distribui\u00e7\u00e3o cumulativa de uma vari\u00e1vel aleat\u00f3ria definida por uma distribui\u00e7\u00e3o gama \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-6bc3247a247daec5048c409319dc3943_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle F(x)=\\int_0^x\\frac{\\lambda(\\lambda y)^{\\alpha-1}e^{-\\lambda y}}{\\Gamma(\\alpha)}\\;dy\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"224\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Se o par\u00e2metro de forma \u03b1 for igual a 1, ent\u00e3o a distribui\u00e7\u00e3o gama \u00e9 equivalente a uma distribui\u00e7\u00e3o exponencial com o mesmo par\u00e2metro de escala \u03bb.<\/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-60ed376f92f0db2c22e19f85bb76f828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\Gamma(1,\\lambda) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim \\text{Exp}(\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"321\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Quando o par\u00e2metro de escala \u03bb \u00e9 uma m\u00e9dia, ent\u00e3o a distribui\u00e7\u00e3o gama \u00e9 um caso especial da <a href=\"https:\/\/statorials.org\/pt\/distribuicao-qui-quadrado\/\">distribui\u00e7\u00e3o qui-quadrado<\/a> .<\/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-efb733464c432d7d1b22ed7e5c534979_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X\\sim \\Gamma\\left(\\frac{n}{2},\\frac{1}{2}\\right) \\text{con } n\\in \\mathbb{N}\\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim \\chi_n^2\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"389\" style=\"vertical-align: -17px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o gama e para que ela \u00e9 usada. Assim, voc\u00ea encontrar\u00e1 a defini\u00e7\u00e3o da distribui\u00e7\u00e3o gama, suas propriedades e como \u00e9 sua representa\u00e7\u00e3o gr\u00e1fica. Qual \u00e9 a distribui\u00e7\u00e3o gama? A distribui\u00e7\u00e3o gama \u00e9 uma distribui\u00e7\u00e3o de probabilidade cont\u00ednua definida por dois par\u00e2metros caracter\u00edsticos, \u03b1 e \u03bb. Em outras [&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-223","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 gama<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 distribui\u00e7\u00e3o gama, para que serve, seu gr\u00e1fico e as caracter\u00edsticas da distribui\u00e7\u00e3o gama.\" \/>\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-gama\/\" \/>\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 gama\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 distribui\u00e7\u00e3o gama, para que serve, seu gr\u00e1fico e as caracter\u00edsticas da distribui\u00e7\u00e3o gama.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-gama\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T23:58:33+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1b0ab2e724ffd74455d0907b39f4a598_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=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-gama\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-gama\/\",\"name\":\"\u25b7 Distribui\u00e7\u00e3o gama\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T23:58:33+00:00\",\"dateModified\":\"2023-08-03T23:58:33+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 distribui\u00e7\u00e3o gama, para que serve, seu gr\u00e1fico e as caracter\u00edsticas da distribui\u00e7\u00e3o gama.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-gama\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-gama\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-gama\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribui\u00e7\u00e3o gama\"}]},{\"@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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