{"id":227,"date":"2023-08-03T22:21:12","date_gmt":"2023-08-03T22:21:12","guid":{"rendered":"https:\/\/statorials.org\/pt\/registrar-distribuicao-normal\/"},"modified":"2023-08-03T22:21:12","modified_gmt":"2023-08-03T22:21:12","slug":"registrar-distribuicao-normal","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/registrar-distribuicao-normal\/","title":{"rendered":"Distribui\u00e7\u00e3o lognormal"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 distribui\u00e7\u00e3o lognormal nas estat\u00edsticas. Assim, voc\u00ea descobrir\u00e1 quais s\u00e3o as propriedades da distribui\u00e7\u00e3o lognormal e o gr\u00e1fico 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-lognormal\"><\/span> Qual \u00e9 a distribui\u00e7\u00e3o lognormal?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o lognormal<\/strong> , ou <strong>distribui\u00e7\u00e3o lognormal<\/strong> , \u00e9 uma distribui\u00e7\u00e3o de probabilidade que define uma vari\u00e1vel aleat\u00f3ria cujo logaritmo segue uma distribui\u00e7\u00e3o normal.<\/p>\n<p> Portanto, se a vari\u00e1vel X tem distribui\u00e7\u00e3o normal, ent\u00e3o a fun\u00e7\u00e3o exponencial e <sup>x<\/sup> tem distribui\u00e7\u00e3o lognormal.<\/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-216d8f120f09a37cd8f797bb3b115a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Lognormal}(\\mu,\\sigma^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Observe que a distribui\u00e7\u00e3o lognormal s\u00f3 pode ser usada quando os valores das vari\u00e1veis s\u00e3o positivos, pois o logaritmo \u00e9 uma fun\u00e7\u00e3o que leva apenas um argumento positivo.<\/p>\n<p> Entre as diferentes aplica\u00e7\u00f5es da distribui\u00e7\u00e3o lognormal em estat\u00edstica, destacamos a utiliza\u00e7\u00e3o desta distribui\u00e7\u00e3o para analisar investimentos financeiros e realizar an\u00e1lises de confiabilidade.<\/p>\n<p> A distribui\u00e7\u00e3o lognormal tamb\u00e9m \u00e9 conhecida <strong>como distribui\u00e7\u00e3o Tinaut<\/strong> , \u00e0s vezes tamb\u00e9m escrita <strong>como distribui\u00e7\u00e3o lognormal<\/strong> ou <strong>distribui\u00e7\u00e3o log-normal<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-lognormal\"><\/span> Gr\u00e1fico de distribui\u00e7\u00e3o lognormal<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que conhecemos a defini\u00e7\u00e3o da distribui\u00e7\u00e3o lognormal, veremos nesta se\u00e7\u00e3o como a representa\u00e7\u00e3o gr\u00e1fica da distribui\u00e7\u00e3o lognormal varia dependendo dos valores de sua m\u00e9dia aritm\u00e9tica e de seu desvio padr\u00e3o.<\/p>\n<p> O gr\u00e1fico da fun\u00e7\u00e3o densidade da distribui\u00e7\u00e3o lognormal \u00e9 o seguinte: <\/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-lognormale.png\" alt=\"gr\u00e1fico de distribui\u00e7\u00e3o lognormal\" class=\"wp-image-4563\" width=\"675\" height=\"406\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Por outro lado, o gr\u00e1fico de probabilidade cumulativa da distribui\u00e7\u00e3o lognormal \u00e9 o seguinte: <\/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-lognormale-cumulative.png\" alt=\"gr\u00e1fico de probabilidade cumulativa de distribui\u00e7\u00e3o lognormal\" class=\"wp-image-4564\" width=\"675\" height=\"404\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-lognormal\"><\/span> Caracter\u00edsticas da distribui\u00e7\u00e3o lognormal<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A distribui\u00e7\u00e3o lognormal possui as seguintes caracter\u00edsticas:<\/p>\n<ul>\n<li> A distribui\u00e7\u00e3o lognormal \u00e9 definida pelo valor de dois par\u00e2metros, sua m\u00e9dia aritm\u00e9tica \u03bc e sua vari\u00e2ncia \u03c3 <sup>2<\/sup> .<\/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-216d8f120f09a37cd8f797bb3b115a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Lognormal}(\\mu,\\sigma^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> O dom\u00ednio da distribui\u00e7\u00e3o lognormal consiste em n\u00fameros reais positivos, pois o logaritmo n\u00e3o aceita valores negativos ou 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-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 expectativa de uma distribui\u00e7\u00e3o lognormal \u00e9 igual ao n\u00famero e elevado \u00e0 soma da m\u00e9dia mais a vari\u00e2ncia dividida por dois.<\/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-109a1024d530b2993db41f1d7a5a24c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E[X]=e^{\\mu+\\frac{\\sigma^2}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Por outro lado, a vari\u00e2ncia de uma distribui\u00e7\u00e3o lognormal 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-5afc17462bb71082888ab755626b853a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\left(e^{\\sigma^2}-1\\right)\\cdot e^{2\\mu+\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"223\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<ul>\n<li> A moda da distribui\u00e7\u00e3o lognormal \u00e9 equivalente ao n\u00famero e elevado \u00e0 m\u00e9dia 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-21b2bd4c45dca8e305c9ee480d961f4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=e^\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"67\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> O coeficiente de assimetria da distribui\u00e7\u00e3o lognormal pode ser determinado 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-2686fd41c4e28d5c396bf494229a63a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\left(e^{\\sigma^2}+2\\right)\\cdot\\sqrt{e^{\\sigma^2}-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"198\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<ul>\n<li> A f\u00f3rmula para a fun\u00e7\u00e3o densidade da distribui\u00e7\u00e3o lognormal \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-25698732745689402d16ea353a072cc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{1}{\\sigma \\cdot x\\cdot \\sqrt{2 \\pi}}\\cdot \\exp\\left(-\\frac{(\\ln x-\\mu)^2}{2\\sigma^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"347\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> A f\u00f3rmula para a fun\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o lognormal \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-59c2474703bad4805a6a44bd05cf92bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\Phi\\left(\\frac{\\ln x-\\mu}{\\sigma}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"200\" style=\"vertical-align: -17px;\"><\/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-21f36758b04341c7980aa18b13ced720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Phi\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a fun\u00e7\u00e3o de probabilidade cumulativa de uma <a href=\"https:\/\/statorials.org\/pt\/distribuicao-padrao-normal\/\">distribui\u00e7\u00e3o normal padr\u00e3o<\/a> .<\/p>\n<ul>\n<li> A m\u00e9dia aritm\u00e9tica de uma distribui\u00e7\u00e3o lognormal \u00e9 maior que o valor de sua mediana.<\/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-96e66e8c60e4ce5e235c30258e4ecead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu > Me&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;16&#8243; width=&#8221;61&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 distribui\u00e7\u00e3o lognormal nas estat\u00edsticas. Assim, voc\u00ea descobrir\u00e1 quais s\u00e3o as propriedades da distribui\u00e7\u00e3o lognormal e o gr\u00e1fico desse tipo de distribui\u00e7\u00e3o de probabilidade. Qual \u00e9 a distribui\u00e7\u00e3o lognormal? A distribui\u00e7\u00e3o lognormal , ou distribui\u00e7\u00e3o lognormal , \u00e9 uma distribui\u00e7\u00e3o de probabilidade que define uma vari\u00e1vel aleat\u00f3ria cujo logaritmo segue [&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-227","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 lognormal<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea aprender\u00e1 o que \u00e9 distribui\u00e7\u00e3o lognormal, quais s\u00e3o as caracter\u00edsticas da distribui\u00e7\u00e3o lognormal e sua representa\u00e7\u00e3o gr\u00e1fica.\" \/>\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\/registrar-distribuicao-normal\/\" \/>\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 lognormal\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea aprender\u00e1 o que \u00e9 distribui\u00e7\u00e3o lognormal, quais s\u00e3o as caracter\u00edsticas da distribui\u00e7\u00e3o lognormal e sua representa\u00e7\u00e3o gr\u00e1fica.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/registrar-distribuicao-normal\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T22:21:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-216d8f120f09a37cd8f797bb3b115a40_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\/registrar-distribuicao-normal\/\",\"url\":\"https:\/\/statorials.org\/pt\/registrar-distribuicao-normal\/\",\"name\":\"\u25b7 Distribui\u00e7\u00e3o lognormal\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T22:21:12+00:00\",\"dateModified\":\"2023-08-03T22:21:12+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea aprender\u00e1 o que \u00e9 distribui\u00e7\u00e3o lognormal, quais s\u00e3o as caracter\u00edsticas da distribui\u00e7\u00e3o lognormal e sua representa\u00e7\u00e3o gr\u00e1fica.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/registrar-distribuicao-normal\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/registrar-distribuicao-normal\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/registrar-distribuicao-normal\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribui\u00e7\u00e3o lognormal\"}]},{\"@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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