{"id":226,"date":"2023-08-03T22:40:38","date_gmt":"2023-08-03T22:40:38","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-weibull\/"},"modified":"2023-08-03T22:40:38","modified_gmt":"2023-08-03T22:40:38","slug":"distribuicao-weibull","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-weibull\/","title":{"rendered":"Distribui\u00e7\u00e3o weibull"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o Weibull e para que \u00e9 usada. Al\u00e9m disso, voc\u00ea poder\u00e1 ver a representa\u00e7\u00e3o gr\u00e1fica da distribui\u00e7\u00e3o Weibull e quais s\u00e3o as propriedades deste tipo de distribui\u00e7\u00e3o de probabilidade. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-de-weibull\"><\/span> Qual \u00e9 a distribui\u00e7\u00e3o Weibull?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o Weibull<\/strong> \u00e9 uma distribui\u00e7\u00e3o de probabilidade cont\u00ednua definida por dois par\u00e2metros caracter\u00edsticos: o par\u00e2metro de forma \u03b1 e o par\u00e2metro de escala \u03bb.<\/p>\n<p> Nas estat\u00edsticas, a distribui\u00e7\u00e3o Weibull \u00e9 usada principalmente para an\u00e1lise de sobreviv\u00eancia. Da mesma forma, a distribui\u00e7\u00e3o Weibull tem muitas aplica\u00e7\u00f5es em diferentes campos. Entraremos em detalhes sobre o uso da distribui\u00e7\u00e3o Weibull abaixo.<\/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> Segundo os autores, a distribui\u00e7\u00e3o Weibull tamb\u00e9m pode ser parametrizada com tr\u00eas par\u00e2metros. Em seguida, \u00e9 adicionado um terceiro par\u00e2metro denominado valor limite, que indica a abcissa na qual o gr\u00e1fico de distribui\u00e7\u00e3o come\u00e7a.<\/p>\n<p> A distribui\u00e7\u00e3o Weibull recebeu o nome do sueco Waloddi Weibull, que a descreveu detalhadamente em 1951. No entanto, a distribui\u00e7\u00e3o Weibull foi descoberta por Maurice Fr\u00e9chet em 1927 e aplicada pela primeira vez por Rosin e Rammler em 1933. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-de-weibull\"><\/span> Tra\u00e7ando a distribui\u00e7\u00e3o Weibull<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos a defini\u00e7\u00e3o da distribui\u00e7\u00e3o Weibull, veremos como sua representa\u00e7\u00e3o gr\u00e1fica varia em fun\u00e7\u00e3o dos valores de seus par\u00e2metros.<\/p>\n<p> Abaixo voc\u00ea pode ver v\u00e1rios exemplos de como o gr\u00e1fico da fun\u00e7\u00e3o densidade da distribui\u00e7\u00e3o Weibull varia dependendo do valor 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\/graphique-de-distribution-de-weibull.png\" alt=\"gr\u00e1fico da distribui\u00e7\u00e3o Weibull\" class=\"wp-image-4592\" width=\"613\" height=\"403\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Quando a distribui\u00e7\u00e3o Weibull \u00e9 usada para modelar a taxa de falha de um sistema em fun\u00e7\u00e3o do tempo, o valor do par\u00e2metro de forma \u03b1 significa o seguinte:<\/p>\n<ul>\n<li> \u03b1&lt;1: a taxa de falha diminui com o tempo.<\/li>\n<li> \u03b1=1: a taxa de falhas \u00e9 constante ao longo do tempo.<\/li>\n<li> \u03b1&gt;1: a taxa de falha aumenta com o tempo.<\/li>\n<\/ul>\n<p> Por outro lado, no gr\u00e1fico a seguir voc\u00ea pode ver a fun\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o Weibull tra\u00e7ada com base em 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-de-probabilite-cumulative-weibull.png\" alt=\"probabilidade cumulativa da distribui\u00e7\u00e3o Weibull\" 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> Caracter\u00edsticas da distribui\u00e7\u00e3o Weibull<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A distribui\u00e7\u00e3o Weibull possui as seguintes caracter\u00edsticas:<\/p>\n<ul>\n<li> A distribui\u00e7\u00e3o Weibull possui dois par\u00e2metros caracter\u00edsticos que definem seu gr\u00e1fico: o par\u00e2metro de forma \u03b1 e o par\u00e2metro de escala \u03bb. Ambos os par\u00e2metros s\u00e3o n\u00fameros reais 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-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> A distribui\u00e7\u00e3o Weibull aceita apenas valores de abcissas 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 Weibull \u00e9 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-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> Por outro lado, a f\u00f3rmula para encontrar a vari\u00e2ncia da distribui\u00e7\u00e3o Weibull \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-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> A moda de uma vari\u00e1vel aleat\u00f3ria que segue uma distribui\u00e7\u00e3o Weibull com \u03b1&gt;1 pode ser determinada pela 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-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> A f\u00f3rmula para a fun\u00e7\u00e3o densidade da distribui\u00e7\u00e3o Weibull \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-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> Da mesma forma, a f\u00f3rmula para a fun\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o Weibull \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-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> O coeficiente de assimetria da distribui\u00e7\u00e3o Weibull \u00e9 calculado 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-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> Por \u00faltimo, a f\u00f3rmula que permite determinar o coeficiente de curtose da distribui\u00e7\u00e3o Weibull \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-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> Ouro <\/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> Aplica\u00e7\u00f5es da distribui\u00e7\u00e3o Weibull<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A distribui\u00e7\u00e3o Weibull tem muitas aplica\u00e7\u00f5es, incluindo:<\/p>\n<ul>\n<li> Na estat\u00edstica aplicada, a distribui\u00e7\u00e3o Weibull \u00e9 utilizada na an\u00e1lise de sobreviv\u00eancia.<\/li>\n<li> Na engenharia, a distribui\u00e7\u00e3o Weibull \u00e9 usada para modelar fun\u00e7\u00f5es relacionadas ao tempo de fabrica\u00e7\u00e3o.<\/li>\n<li> Em sistemas de radar, para simular a dispers\u00e3o do sinal recebido.<\/li>\n<li> No setor de seguros, para modelar a extens\u00e3o dos sinistros.<\/li>\n<li> Em meteorologia, por exemplo, para modelar a frequ\u00eancia de diferentes velocidades do vento.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o Weibull e para que \u00e9 usada. Al\u00e9m disso, voc\u00ea poder\u00e1 ver a representa\u00e7\u00e3o gr\u00e1fica da distribui\u00e7\u00e3o Weibull e quais s\u00e3o as propriedades deste tipo de distribui\u00e7\u00e3o de probabilidade. Qual \u00e9 a distribui\u00e7\u00e3o Weibull? A distribui\u00e7\u00e3o Weibull \u00e9 uma distribui\u00e7\u00e3o de probabilidade cont\u00ednua definida por dois par\u00e2metros caracter\u00edsticos: [&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-226","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>\u25b7Distribui\u00e7\u00e3o Weibull<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o Weibull, seu gr\u00e1fico, caracter\u00edsticas da distribui\u00e7\u00e3o Weibull e suas aplica\u00e7\u00f5es.\" \/>\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-weibull\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7Distribui\u00e7\u00e3o Weibull\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o Weibull, seu gr\u00e1fico, caracter\u00edsticas da distribui\u00e7\u00e3o Weibull e suas aplica\u00e7\u00f5es.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-weibull\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T22:40:38+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-14be9904756b25df209befbae173e29e_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-weibull\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-weibull\/\",\"name\":\"\u25b7Distribui\u00e7\u00e3o Weibull\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T22:40:38+00:00\",\"dateModified\":\"2023-08-03T22:40:38+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o Weibull, seu gr\u00e1fico, caracter\u00edsticas da distribui\u00e7\u00e3o Weibull e suas aplica\u00e7\u00f5es.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-weibull\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-weibull\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-weibull\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribui\u00e7\u00e3o weibull\"}]},{\"@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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