{"id":2967,"date":"2023-07-19T20:57:51","date_gmt":"2023-07-19T20:57:51","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-normal-bivariada-em-r\/"},"modified":"2023-07-19T20:57:51","modified_gmt":"2023-07-19T20:57:51","slug":"distribuicao-normal-bivariada-em-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-normal-bivariada-em-r\/","title":{"rendered":"Como simular e tra\u00e7ar uma distribui\u00e7\u00e3o normal bivariada em r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><span style=\"color: #000000;\">Nas estat\u00edsticas, duas vari\u00e1veis seguem uma <strong>distribui\u00e7\u00e3o normal bivariada<\/strong> se tiverem uma distribui\u00e7\u00e3o normal quando somadas.<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Este tutorial explica como executar as seguintes tarefas em R:<\/span><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Simular uma distribui\u00e7\u00e3o normal bivariada<\/span><\/li>\n<li> <span style=\"color: #000000;\">Trace uma distribui\u00e7\u00e3o normal bivariada usando um gr\u00e1fico de contorno (gr\u00e1fico 2D)<\/span><\/li>\n<li> <span style=\"color: #000000;\">Trace uma distribui\u00e7\u00e3o normal bivariada usando um gr\u00e1fico de superf\u00edcie (gr\u00e1fico 3D)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Vamos!<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo 1: Simule uma distribui\u00e7\u00e3o normal bivariada em R<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">A maneira mais simples de simular uma distribui\u00e7\u00e3o normal bivariada em R \u00e9 usar a fun\u00e7\u00e3o <strong>mvrnorm()<\/strong> do pacote <strong>MASS<\/strong> .<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como usar esta fun\u00e7\u00e3o para simular uma distribui\u00e7\u00e3o normal bivariada na pr\u00e1tica:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">library<\/span> (MASS)\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>set. <span style=\"color: #3366ff;\">seed<\/span> ( <span style=\"color: #008000;\">0<\/span> )\n\n<span style=\"color: #008080;\">#simulate bivariate normal distribution\n<\/span>bivariate_data &lt;- as. <span style=\"color: #3366ff;\">data<\/span> . <span style=\"color: #3366ff;\">frame<\/span> (mvrnorm(n= <span style=\"color: #008000;\">100<\/span> ,\n                                        mu=c(0, 0),\n                                        Sigma=matrix(c(5, 3, 4, 4), ncol= <span style=\"color: #008000;\">2<\/span> )))\n\n<span style=\"color: #008080;\">#view first six rows of bivariate dataset\n<\/span>head(bivariate_data)\n\n           V1 V2\n1 -2.03600343 -2.9623059\n2 0.07719131 1.2948982\n3 -3.26729701 -1.7928069\n4 -2.62985132 -2.3015471\n5 -1.75126215 0.3056698\n6 3.67698436 2.2020238\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Aqui est\u00e1 o que cada argumento da fun\u00e7\u00e3o <strong>mvrnorm()<\/strong> faz:<\/span><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> : Define o tamanho da amostra<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>mu<\/strong> : Define a m\u00e9dia de cada vari\u00e1vel<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Sigma<\/strong> : Define a matriz de covari\u00e2ncia das duas vari\u00e1veis<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O resultado final \u00e9 um quadro de dados com duas vari\u00e1veis que segue uma distribui\u00e7\u00e3o normal quando somadas.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo 2:<\/strong><\/span> <span style=\"color: #000000;\"><strong>tra\u00e7ando uma distribui\u00e7\u00e3o normal bivariada<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A maneira mais f\u00e1cil de tra\u00e7ar uma distribui\u00e7\u00e3o normal bivariada em R \u00e9 usar as fun\u00e7\u00f5es do pacote <strong>mnormt()<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, podemos usar a fun\u00e7\u00e3o <strong>contorno()<\/strong> deste pacote para criar um gr\u00e1fico de contorno, que fornece uma visualiza\u00e7\u00e3o 2D da distribui\u00e7\u00e3o normal bivariada:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">library<\/span> (mnormt)\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>set. <span style=\"color: #3366ff;\">seed<\/span> ( <span style=\"color: #008000;\">0<\/span> )\n\n<span style=\"color: #008080;\">#create bivariate normal distribution\n<\/span>x &lt;- seq(-3, 3, 0.1) \ny &lt;- seq(-3, 3, 0.1)\nmu &lt;- c(0, 0)\nsigma &lt;- matrix(c(2, -1, -1, 2), nrow= <span style=\"color: #008000;\">2<\/span> )\nf &lt;- function(x, y) dmnorm(cbind(x, y), mu, sigma)\nz &lt;- outer(x, y, f)\n\n<span style=\"color: #008080;\">#create contour plot\n<\/span>contour(x, y, z)\n<\/strong><\/span><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-25707\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/bivar1.jpg\" alt=\"gr\u00e1fico de contorno normal bivariado em R\" width=\"448\" height=\"413\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Tamb\u00e9m podemos usar a fun\u00e7\u00e3o <strong>persp()<\/strong> para criar um gr\u00e1fico de superf\u00edcie, que fornece uma visualiza\u00e7\u00e3o 3D da distribui\u00e7\u00e3o normal bivariada:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">library<\/span> (mnormt)\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>set. <span style=\"color: #3366ff;\">seed<\/span> ( <span style=\"color: #008000;\">0<\/span> )\n\n<span style=\"color: #008080;\">#create bivariate normal distribution\n<\/span>x &lt;- seq(-3, 3, 0.1) \ny &lt;- seq(-3, 3, 0.1)\nmu &lt;- c(0, 0)\nsigma &lt;- matrix(c(2, -1, -1, 2), nrow= <span style=\"color: #008000;\">2<\/span> )\nf &lt;- function(x, y) dmnorm(cbind(x, y), mu, sigma)\nz &lt;- outer(x, y, f)\n\n<span style=\"color: #008080;\">#create surface plot\n<\/span>persp(x, y, z, theta= <span style=\"color: #008000;\">-30<\/span> , phi= <span style=\"color: #008000;\">25<\/span> , expand= <span style=\"color: #008000;\">0.6<\/span> , ticktype=' <span style=\"color: #ff0000;\">detailed<\/span> ')\n<\/strong><\/span><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-25708\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/bivar2.jpg\" alt=\"gr\u00e1fico de superf\u00edcie de distribui\u00e7\u00e3o normal bivariada em R\" width=\"447\" height=\"384\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Aqui est\u00e1 o que cada argumento da fun\u00e7\u00e3o <strong>persp()<\/strong> faz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>theta, phi<\/strong> : Define os \u00e2ngulos de dire\u00e7\u00e3o de visualiza\u00e7\u00e3o.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>expandir<\/strong> : controla o tamanho do eixo z.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>ticktype<\/strong> : Controla a apar\u00eancia dos ticks nos eixos.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O resultado final \u00e9 um gr\u00e1fico de superf\u00edcie 3D da distribui\u00e7\u00e3o normal bivariada.<\/span><\/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 de probabilidade em R:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pt\/dnorm-pnorm-rnorm-qnorm-em-r\/\" target=\"_blank\" rel=\"noopener\">Como usar a distribui\u00e7\u00e3o normal em R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/dbinom-pbinom-qbinom-rbinom-em-r\/\" target=\"_blank\" rel=\"noopener\">Como usar distribui\u00e7\u00e3o binomial em R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/ppois-ppois-qpois-rpois-r\/\" target=\"_blank\" rel=\"noopener\">Como usar a distribui\u00e7\u00e3o de Poisson em R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-multinomial-em-r\/\" target=\"_blank\" rel=\"noopener\">Como usar distribui\u00e7\u00e3o multinomial em R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nas estat\u00edsticas, duas vari\u00e1veis seguem uma distribui\u00e7\u00e3o normal bivariada se tiverem uma distribui\u00e7\u00e3o normal quando somadas. Este tutorial explica como executar as seguintes tarefas em R: Simular uma distribui\u00e7\u00e3o normal bivariada Trace uma distribui\u00e7\u00e3o normal bivariada usando um gr\u00e1fico de contorno (gr\u00e1fico 2D) Trace uma distribui\u00e7\u00e3o normal bivariada usando um gr\u00e1fico de superf\u00edcie (gr\u00e1fico 3D) [&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-2967","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 simular e tra\u00e7ar uma distribui\u00e7\u00e3o normal bivariada em R - Estatologia<\/title>\n<meta name=\"description\" content=\"Este tutorial explica como simular e tra\u00e7ar uma distribui\u00e7\u00e3o normal bivariada em R, 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-normal-bivariada-em-r\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como simular e tra\u00e7ar uma distribui\u00e7\u00e3o normal bivariada em R - 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