{"id":229,"date":"2023-08-03T21:54:17","date_gmt":"2023-08-03T21:54:17","guid":{"rendered":"https:\/\/statorials.org\/pt\/lei-de-pareto\/"},"modified":"2023-08-03T21:54:17","modified_gmt":"2023-08-03T21:54:17","slug":"lei-de-pareto","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/lei-de-pareto\/","title":{"rendered":"Distribui\u00e7\u00e3o de pareto"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o de Pareto nas estat\u00edsticas e para que ela \u00e9 usada. Voc\u00ea tamb\u00e9m poder\u00e1 ver o gr\u00e1fico da distribui\u00e7\u00e3o de Pareto e as propriedades desse 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-pareto\"><\/span> O que \u00e9 distribui\u00e7\u00e3o de Pareto?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o de Pareto<\/strong> \u00e9 uma distribui\u00e7\u00e3o de probabilidade cont\u00ednua usada em estat\u00edstica para modelar o princ\u00edpio de Pareto. Portanto, a distribui\u00e7\u00e3o de Pareto \u00e9 uma distribui\u00e7\u00e3o de probabilidade que possui alguns valores cuja probabilidade de ocorr\u00eancia \u00e9 muito maior que o restante dos valores.<\/p>\n<p> Lembre-se que a lei de Pareto, tamb\u00e9m chamada de regra 80-20, \u00e9 um princ\u00edpio estat\u00edstico que diz que a maior parte da causa de um fen\u00f4meno se deve a uma pequena parte da popula\u00e7\u00e3o.<\/p>\n<p> A distribui\u00e7\u00e3o de Pareto possui dois par\u00e2metros caracter\u00edsticos: o par\u00e2metro de escala x <sub>m<\/sub> e o par\u00e2metro de forma \u03b1.<\/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-c13a66a388e0a7e26781a0e8d9645f40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Pareto}(\\alpha,x_m)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Originalmente, a distribui\u00e7\u00e3o de Pareto era usada para descrever a distribui\u00e7\u00e3o da riqueza dentro da popula\u00e7\u00e3o, porque a maior parte dela se devia a uma pequena propor\u00e7\u00e3o da popula\u00e7\u00e3o. Mas actualmente a distribui\u00e7\u00e3o de Pareto tem muitas aplica\u00e7\u00f5es, por exemplo no controlo de qualidade, na economia, na ci\u00eancia, no campo social, etc.<\/p>\n<p> A distribui\u00e7\u00e3o de Pareto leva o nome do economista Vilfredo Pareto, que formulou a distribui\u00e7\u00e3o. No entanto, ele \u00e9 mais conhecido pelo gr\u00e1fico de Pareto. <\/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\/diagrama-de-pareto\/\">O que \u00e9 o gr\u00e1fico de Pareto?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-de-pareto\"><\/span> Tabela de distribui\u00e7\u00e3o de Pareto<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que conhecemos a defini\u00e7\u00e3o de distribui\u00e7\u00e3o de Pareto, vejamos v\u00e1rios exemplos de distribui\u00e7\u00f5es de Pareto representadas graficamente.<\/p>\n<p> Assim, a seguir voc\u00ea pode ver como fica o gr\u00e1fico da fun\u00e7\u00e3o densidade da distribui\u00e7\u00e3o de Pareto dependendo de seus valores caracter\u00edsticos: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/graphique-de-distribution-de-pareto.png\" alt=\"Gr\u00e1fico de distribui\u00e7\u00e3o de Pareto\" class=\"wp-image-4774\" width=\"587\" height=\"413\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Observe que o dom\u00ednio da distribui\u00e7\u00e3o de Pareto vai do valor x <sub>m<\/sub> at\u00e9 +\u221e, raz\u00e3o pela qual a fun\u00e7\u00e3o densidade n\u00e3o existe antes do valor de x <sub>m<\/sub> .<\/p>\n<p> Por outro lado, o gr\u00e1fico da fun\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o de Pareto \u00e9 o seguinte: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-de-probabilite-pareto-cumulative.png\" alt=\"probabilidade cumulativa da distribui\u00e7\u00e3o de Pareto\" class=\"wp-image-4775\" width=\"589\" height=\"414\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-de-pareto\"><\/span> Caracter\u00edsticas da distribui\u00e7\u00e3o de Pareto<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Abaixo est\u00e3o as caracter\u00edsticas mais importantes da distribui\u00e7\u00e3o de Pareto relacionadas \u00e0 teoria de probabilidade e estat\u00edstica.<\/p>\n<ul>\n<li> A distribui\u00e7\u00e3o de Pareto possui dois par\u00e2metros caracter\u00edsticos que definem sua curva: o par\u00e2metro de escala x <sub>m<\/sub> e o par\u00e2metro de forma \u03b1.<\/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-c13a66a388e0a7e26781a0e8d9645f40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Pareto}(\\alpha,x_m)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> O dom\u00ednio da distribui\u00e7\u00e3o de Pareto consiste em todos os n\u00fameros reais desde o par\u00e2metro de escala at\u00e9 mais o infinito.<\/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-c720ee182b49a794ed2862dd83a10ca9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in [x_m,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Se \u03b1 for maior que 1, a m\u00e9dia da distribui\u00e7\u00e3o de Pareto \u00e9 igual ao produto de \u03b1 vezes x <sub>m<\/sub> e \u03b1 menos 1.<\/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-6d26513868f9ed6fa45ab0fde0030884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{\\alpha\\cdot x_m}{\\alpha-1}\\quad\\text{para } \\alpha>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;34&#8243; width=&#8221;214&#8243; style=&#8221;vertical-align: -12px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> A vari\u00e2ncia da distribui\u00e7\u00e3o de Pareto depende dos dois par\u00e2metros caracter\u00edsticos da distribui\u00e7\u00e3o e \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-6120976b3586b76661d13bb9fdd5375d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Var(X)=\\frac{x_\\mathrm{m}^2\\cdot \\alpha}{(\\alpha-1)^2\\cdot(\\alpha-2)}\\quad \\text{para }\\alpha>2&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;44&#8243; width=&#8221;323&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> A mediana da distribui\u00e7\u00e3o de Pareto pode ser determinada 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-0dc2c772a0a0662ad05f8b22c3cf1ba1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Me=x_\\mathrm{m}\\cdot \\sqrt[\\alpha]{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"113\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> A moda da distribui\u00e7\u00e3o de Pareto \u00e9 equivalente ao par\u00e2metro de escala x <sub>m<\/sub> da distribui\u00e7\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-494f2f6e64851f90c504c989d93e22dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=x_m\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> A f\u00f3rmula para a fun\u00e7\u00e3o densidade da distribui\u00e7\u00e3o de Pareto \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-1e182771cfe3bf9a145a2ee59b9c7eeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{\\alpha\\cdot x_m^\\alpha}{x^{\\alpha+1}}\\quad\\text{para }x\\geq x_m\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"262\" style=\"vertical-align: -12px;\"><\/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 de Pareto \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-480adc7841b7c72cb4bfecb446ed3fab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=1-\\left(\\frac{x_\\mathrm{m}}{x}\\right)^\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> O coeficiente de assimetria da distribui\u00e7\u00e3o de Pareto depende apenas do par\u00e2metro de forma \u03b1 e sua express\u00e3o \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-98e7ba5f5d32988033c0f33d6af1bef8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\frac{2(1+\\alpha)}{\\alpha-3}\\,\\sqrt{\\frac{\\alpha-2}{\\alpha}}\\quad\\text{para }\\alpha>3&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;43&#8243; width=&#8221;274&#8243; style=&#8221;vertical-align: -14px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> O coeficiente de curtose da distribui\u00e7\u00e3o de Pareto tamb\u00e9m varia dependendo do valor do par\u00e2metro \u03b1 e \u00e9 calculado pela 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-989019815fbeb266226cff9aa6b4a52b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\frac{6(\\alpha^3+\\alpha^2-6\\alpha-2)}{\\alpha(\\alpha-3)(\\alpha-4)}\\quad\\text{para }\\alpha>4&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;44&#8243; width=&#8221;299&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o de Pareto nas estat\u00edsticas e para que ela \u00e9 usada. Voc\u00ea tamb\u00e9m poder\u00e1 ver o gr\u00e1fico da distribui\u00e7\u00e3o de Pareto e as propriedades desse tipo de distribui\u00e7\u00e3o de probabilidade. O que \u00e9 distribui\u00e7\u00e3o de Pareto? A distribui\u00e7\u00e3o de Pareto \u00e9 uma distribui\u00e7\u00e3o de probabilidade cont\u00ednua usada em [&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-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 de Pareto<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea aprender\u00e1 o que \u00e9 a distribui\u00e7\u00e3o de Pareto, para que serve, seu gr\u00e1fico e quais s\u00e3o as propriedades da distribui\u00e7\u00e3o de Pareto.\" \/>\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\/lei-de-pareto\/\" \/>\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 de Pareto\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea aprender\u00e1 o que \u00e9 a distribui\u00e7\u00e3o de Pareto, para que serve, seu gr\u00e1fico e quais s\u00e3o as propriedades da distribui\u00e7\u00e3o de Pareto.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/lei-de-pareto\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T21:54:17+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c13a66a388e0a7e26781a0e8d9645f40_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\/lei-de-pareto\/\",\"url\":\"https:\/\/statorials.org\/pt\/lei-de-pareto\/\",\"name\":\"\u25b7 Distribui\u00e7\u00e3o de Pareto\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T21:54:17+00:00\",\"dateModified\":\"2023-08-03T21:54:17+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea aprender\u00e1 o que \u00e9 a distribui\u00e7\u00e3o de Pareto, para que serve, seu gr\u00e1fico e quais s\u00e3o as propriedades da distribui\u00e7\u00e3o de Pareto.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/lei-de-pareto\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/lei-de-pareto\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/lei-de-pareto\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribui\u00e7\u00e3o de pareto\"}]},{\"@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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