{"id":3118,"date":"2023-07-19T03:24:49","date_gmt":"2023-07-19T03:24:49","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-exponencial-python\/"},"modified":"2023-07-19T03:24:49","modified_gmt":"2023-07-19T03:24:49","slug":"distribuicao-exponencial-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-exponencial-python\/","title":{"rendered":"Como usar distribui\u00e7\u00e3o exponencial em python"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">A <a href=\"https:\/\/statorials.org\/pt\/distribuicao-exponencial-1\/\" target=\"_blank\" rel=\"noopener\">distribui\u00e7\u00e3o exponencial<\/a> \u00e9 uma distribui\u00e7\u00e3o de probabilidade usada para modelar o tempo que temos que esperar at\u00e9 que um determinado evento ocorra.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Se uma <a href=\"https:\/\/statorials.org\/pt\/variaveis-aleatorias\/\" target=\"_blank\" rel=\"noopener\">vari\u00e1vel aleat\u00f3ria<\/a> <em>X<\/em> segue uma distribui\u00e7\u00e3o exponencial, ent\u00e3o a<\/span> <span style=\"color: #000000;\">fun\u00e7\u00e3o de distribui\u00e7\u00e3o cumulativa de <em>X<\/em> pode ser escrita:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>F<\/em> (x; \u03bb) = 1 \u2013 e <sup>-\u03bbx<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03bb:<\/strong> o par\u00e2metro de taxa (calculado como \u03bb = 1\/\u03bc)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>e:<\/strong> Uma constante aproximadamente igual a 2,718<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Este tutorial explica como usar a distribui\u00e7\u00e3o exponencial em Python.<\/span><\/p>\n<h3> <strong>Como gerar uma distribui\u00e7\u00e3o exponencial<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Voc\u00ea pode usar a fun\u00e7\u00e3o <strong>expon.rvs(scale, size)<\/strong> da biblioteca SciPy em Python para gerar valores aleat\u00f3rios de uma distribui\u00e7\u00e3o exponencial com um par\u00e2metro de taxa e tamanho de amostra espec\u00edficos:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> expo\n\n<span style=\"color: #008080;\">#generate random values from exponential distribution with rate=40 and sample size=10<\/span>\nexpon. <span style=\"color: #3366ff;\">rvs<\/span> (scale= <span style=\"color: #008000;\">40<\/span> , size= <span style=\"color: #008000;\">10<\/span> )\n\narray([116.5368323 , 67.23514699, 12.00399043, 40.74580584,\n        34.60922432, 2.68266663, 22.70459831, 97.66661811,\n         6.64272914, 46.15547298])\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Nota<\/strong> : Voc\u00ea pode encontrar a documenta\u00e7\u00e3o completa da biblioteca SciPy <a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.expon.html\" target=\"_blank\" rel=\"noopener\">aqui<\/a> .<\/span><\/p>\n<h3> <strong>Como calcular probabilidades usando uma distribui\u00e7\u00e3o exponencial<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que o n\u00famero m\u00e9dio de minutos entre as erup\u00e7\u00f5es de um determinado g\u00eaiser seja de 40 minutos. Qual \u00e9 a probabilidade de termos de esperar menos de 50 minutos por uma erup\u00e7\u00e3o?<\/span><\/p>\n<p> <span style=\"color: #000000;\">Para resolver este problema, primeiro precisamos calcular o par\u00e2metro de taxa:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u03bb = 1\/\u00b5<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03bb = 1\/40<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03bb = 0,025<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Podemos inserir \u03bb = 0,025 e x = 50 na f\u00f3rmula CDF:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(X \u2264 x) = 1 \u2013 e <sup>-\u03bbx<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X \u2264 50) = 1 \u2013 e <sup>-0,025(50)<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X \u2264 50) = 0,7135<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A probabilidade de termos que esperar menos de 50 minutos pela pr\u00f3xima erup\u00e7\u00e3o \u00e9 <strong>de 0,7135<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos usar a fun\u00e7\u00e3o <strong>expon.cdf()<\/strong> do SciPy para resolver este problema em Python:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> expo\n\n<span style=\"color: #008080;\">#calculate probability that x is less than 50 when mean rate is 40<\/span>\nexpon. <span style=\"color: #3366ff;\">cdf<\/span> (x=50, scale=40)\n\n0.7134952031398099\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A probabilidade de termos que esperar menos de 50 minutos pela pr\u00f3xima erup\u00e7\u00e3o \u00e9 <strong>de 0,7135<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Isso corresponde ao valor que calculamos manualmente.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Como tra\u00e7ar uma distribui\u00e7\u00e3o exponencial<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Voc\u00ea pode usar a seguinte sintaxe para tra\u00e7ar uma distribui\u00e7\u00e3o exponencial com um determinado par\u00e2metro de taxa:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> expo\n<span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n\n<span style=\"color: #008080;\">#generate exponential distribution with sample size 10000<\/span>\nx = expon. <span style=\"color: #3366ff;\">rvs<\/span> (scale= <span style=\"color: #008000;\">40<\/span> ,size= <span style=\"color: #008000;\">10000<\/span> )\n\n<span style=\"color: #008080;\">#create plot of exponential distribution\n<\/span>plt. <span style=\"color: #3366ff;\">hist<\/span> (x, density= <span style=\"color: #008000;\">True<\/span> , edgecolor=' <span style=\"color: #ff0000;\">black<\/span> ')\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-26590 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exponentielpython1.jpg\" alt=\"\" width=\"514\" height=\"388\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Os tutoriais a seguir explicam como usar outras distribui\u00e7\u00f5es comuns em Python:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-de-peixes-python\/\" target=\"_blank\" rel=\"noopener\">Como usar a distribui\u00e7\u00e3o Poisson em Python<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-python\/\" target=\"_blank\" rel=\"noopener\">Como usar a distribui\u00e7\u00e3o t em Python<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-uniforme-python\/\" target=\"_blank\" rel=\"noopener\">Como usar distribui\u00e7\u00e3o uniforme em Python<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A distribui\u00e7\u00e3o exponencial \u00e9 uma distribui\u00e7\u00e3o de probabilidade usada para modelar o tempo que temos que esperar at\u00e9 que um determinado evento ocorra. Se uma vari\u00e1vel aleat\u00f3ria X segue uma distribui\u00e7\u00e3o exponencial, ent\u00e3o a fun\u00e7\u00e3o de distribui\u00e7\u00e3o cumulativa de X pode ser escrita: F (x; \u03bb) = 1 \u2013 e -\u03bbx Ouro: \u03bb: o par\u00e2metro [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-3118","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Como usar a distribui\u00e7\u00e3o exponencial em Python - Estatologia<\/title>\n<meta name=\"description\" content=\"Este tutorial explica como usar a distribui\u00e7\u00e3o exponencial em Python, com v\u00e1rios exemplos.\" \/>\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-exponencial-python\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como usar a distribui\u00e7\u00e3o exponencial em Python - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Este tutorial explica como usar a distribui\u00e7\u00e3o exponencial em Python, com v\u00e1rios exemplos.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-exponencial-python\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-19T03:24:49+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exponentielpython1.jpg\" \/>\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-exponencial-python\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-exponencial-python\/\",\"name\":\"Como usar a distribui\u00e7\u00e3o exponencial em Python - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-19T03:24:49+00:00\",\"dateModified\":\"2023-07-19T03:24:49+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial explica como usar a distribui\u00e7\u00e3o exponencial em Python, com v\u00e1rios exemplos.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-exponencial-python\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-exponencial-python\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-exponencial-python\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como usar distribui\u00e7\u00e3o exponencial em python\"}]},{\"@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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