{"id":1346,"date":"2023-07-26T19:00:35","date_gmt":"2023-07-26T19:00:35","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-rayleigh\/"},"modified":"2023-07-26T19:00:35","modified_gmt":"2023-07-26T19:00:35","slug":"distribuicao-rayleigh","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-rayleigh\/","title":{"rendered":"Uma introdu\u00e7\u00e3o \u00e0 distribui\u00e7\u00e3o rayleigh"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">A <strong>distribui\u00e7\u00e3o Rayleigh<\/strong> \u00e9 uma distribui\u00e7\u00e3o de probabilidade cont\u00ednua usada para modelar <a href=\"https:\/\/statorials.org\/pt\/variaveis-aleatorias\/\" target=\"_blank\" rel=\"noopener\">vari\u00e1veis aleat\u00f3rias<\/a> que s\u00f3 podem assumir valores iguais ou maiores que zero.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tem a seguinte fun\u00e7\u00e3o de densidade de probabilidade:<\/span><\/p>\n<p> <span style=\"color: #000000;\">f(x; \u03c3) = (x\/\u03c3 <sup>2<\/sup> )e <sup>-x <sup>2<\/sup> \/(2\u03c3 <sup>2<\/sup> )<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">onde \u03c3 \u00e9 o par\u00e2metro de escala da distribui\u00e7\u00e3o.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Propriedades da distribui\u00e7\u00e3o Rayleigh<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A distribui\u00e7\u00e3o Rayleigh tem as seguintes propriedades:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>M\u00e9dia:<\/strong> \u03c3\u221a <span style=\"border-top: 1px solid black;\">\u03c0\/2<\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Desvio:<\/strong> ((4-\u03c0)\/2)\u03c3 <sup>2<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Modo:<\/strong> \u03c3<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Como \u03c0 tem um valor num\u00e9rico conhecido, podemos simplificar as propriedades da seguinte forma:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>M\u00e9dia:<\/strong> 1,253\u03c3<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Desvio:<\/strong> 0,429\u03c3 <sup>2<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Modo:<\/strong> \u03c3<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Visualiza\u00e7\u00e3o da distribui\u00e7\u00e3o Rayleigh<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">O gr\u00e1fico a seguir mostra o formato da distribui\u00e7\u00e3o Rayleigh, pois ela assume valores diferentes para o par\u00e2metro de escala:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13154 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/rayleigh1.png\" alt=\"Distribui\u00e7\u00e3o de probabilidade Rayleigh\" width=\"419\" height=\"377\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Observe que quanto maior o valor do par\u00e2metro de escala \u03c3, mais ampla se torna a distribui\u00e7\u00e3o.<\/span><\/p>\n<p> <em><span style=\"color: #000000;\"><strong>B\u00f4nus:<\/strong> Para quem tiver curiosidade, utilizamos o seguinte c\u00f3digo R para gerar o gr\u00e1fico acima:<\/span><\/em><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load VGAM package\n<\/span><span style=\"color: #008000;\">library<\/span> (VGAM)\n\n<span style=\"color: #008080;\">#create density plots\n<\/span>curve(drayleigh(x, scale = 0.5), from=0, to=10, col='green')\ncurve(drayleigh(x, scale = 1), from=0, to=10, col='red', add=TRUE)\ncurve(drayleigh(x, scale = 2), from=0, to=10, col='blue', add=TRUE)\ncurve(drayleigh(x, scale = 4), from=0, to=10, col='purple', add=TRUE)\n\n<span style=\"color: #008080;\">#add legend\n<\/span>legend(6, 1, legend=c(\"\u03c3=0.5\", \"\u03c3=1\", \"\u03c3=2\", \"\u03c3=4\"),\n       col=c(\"green\", \"red\", \"blue\", \"purple\"), lty=1, cex=1.2)\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Relacionamento com outras distribui\u00e7\u00f5es<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A distribui\u00e7\u00e3o Rayleigh tem a seguinte rela\u00e7\u00e3o com outras distribui\u00e7\u00f5es de probabilidade:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> Quando o par\u00e2metro de escala (\u03c3) \u00e9 igual a <span style=\"color: #000000;\">1, a distribui\u00e7\u00e3o Rayleigh \u00e9 igual a uma distribui\u00e7\u00e3o Qui-quadrado com 2 graus de liberdade.<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> A distribui\u00e7\u00e3o Rayleigh \u00e9 um caso especial da distribui\u00e7\u00e3o Weibull com par\u00e2metro de forma k = 2.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3.<\/strong> A distribui\u00e7\u00e3o Rayleigh com par\u00e2metro de escala \u03c3 \u00e9 igual \u00e0 distribui\u00e7\u00e3o Rice com Rice(0, \u03c3).<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Formul\u00e1rios<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Na pr\u00e1tica, a distribui\u00e7\u00e3o Rayleigh \u00e9 usada em diversas aplica\u00e7\u00f5es, incluindo:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> A distribui\u00e7\u00e3o Rayleigh \u00e9 usada para modelar o comportamento das ondas no oceano, incluindo o tempo que as ondas levam para atingir a crista e a altura m\u00e1xima atingida pelas ondas.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> A distribui\u00e7\u00e3o Rayleigh \u00e9 usada para modelar o comportamento dos dados de fundo em imagens de resson\u00e2ncia magn\u00e9tica, mais comumente conhecidas como MRI.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3.<\/strong> A distribui\u00e7\u00e3o Rayleigh \u00e9 utilizada no campo da nutri\u00e7\u00e3o para modelar a rela\u00e7\u00e3o entre os n\u00edveis de nutrientes e a resposta nutricional em humanos e animais.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Os tutoriais a seguir fornecem informa\u00e7\u00f5es adicionais sobre outras distribui\u00e7\u00f5es em estat\u00edsticas:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pt\/a-distribuicao-normal\/\" target=\"_blank\" rel=\"noopener\">Uma introdu\u00e7\u00e3o \u00e0 distribui\u00e7\u00e3o normal<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-binomial-1\/\" target=\"_blank\" rel=\"noopener\">Uma introdu\u00e7\u00e3o \u00e0 distribui\u00e7\u00e3o binomial<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-de-peixe\/\" target=\"_blank\" rel=\"noopener\">Uma introdu\u00e7\u00e3o \u00e0 distribui\u00e7\u00e3o de Poisson<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A distribui\u00e7\u00e3o Rayleigh \u00e9 uma distribui\u00e7\u00e3o de probabilidade cont\u00ednua usada para modelar vari\u00e1veis aleat\u00f3rias que s\u00f3 podem assumir valores iguais ou maiores que zero. Tem a seguinte fun\u00e7\u00e3o de densidade de probabilidade: f(x; \u03c3) = (x\/\u03c3 2 )e -x 2 \/(2\u03c3 2 ) onde \u03c3 \u00e9 o par\u00e2metro de escala da distribui\u00e7\u00e3o. Propriedades da distribui\u00e7\u00e3o [&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-1346","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>Uma Introdu\u00e7\u00e3o \u00e0 Distribui\u00e7\u00e3o Rayleigh - Estatologia<\/title>\n<meta name=\"description\" content=\"Este tutorial fornece uma introdu\u00e7\u00e3o r\u00e1pida \u00e0 distribui\u00e7\u00e3o Rayleigh, incluindo uma defini\u00e7\u00e3o formal e 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-rayleigh\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Uma Introdu\u00e7\u00e3o \u00e0 Distribui\u00e7\u00e3o Rayleigh - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Este tutorial fornece uma introdu\u00e7\u00e3o r\u00e1pida \u00e0 distribui\u00e7\u00e3o Rayleigh, incluindo uma defini\u00e7\u00e3o formal e v\u00e1rios exemplos.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-rayleigh\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-26T19:00:35+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/rayleigh1.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-rayleigh\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-rayleigh\/\",\"name\":\"Uma Introdu\u00e7\u00e3o \u00e0 Distribui\u00e7\u00e3o Rayleigh - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-26T19:00:35+00:00\",\"dateModified\":\"2023-07-26T19:00:35+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial fornece uma introdu\u00e7\u00e3o r\u00e1pida \u00e0 distribui\u00e7\u00e3o Rayleigh, incluindo uma defini\u00e7\u00e3o formal e v\u00e1rios exemplos.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-rayleigh\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-rayleigh\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-rayleigh\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Uma introdu\u00e7\u00e3o \u00e0 distribui\u00e7\u00e3o rayleigh\"}]},{\"@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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