{"id":3172,"date":"2022-04-16T14:17:04","date_gmt":"2022-04-16T14:17:04","guid":{"rendered":"https:\/\/ricovictor.com\/?p=3172"},"modified":"2026-01-29T21:43:19","modified_gmt":"2026-01-29T21:43:19","slug":"distribucion-t-de-student-en-rstudio","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2022\/04\/16\/distribucion-t-de-student-en-rstudio\/","title":{"rendered":"Distribuci\u00f3n T de STUDENT en Rstudio"},"content":{"rendered":"\n<p>En probabilidad y estad\u00edstica, la <strong>distribuci\u00f3n T de Student es una distribuci\u00f3n de probabilidad <\/strong>que surge del problema de estimar la media de una poblaci\u00f3n normalmente distribuida cuando el tama\u00f1o de la muestra es peque\u00f1o y la desviaci\u00f3n est\u00e1ndar poblacional es desconocida.<\/p>\n\n\n\n<p> La representaci\u00f3n gr\u00e1fica se parece a la distribuci\u00f3n normal, es decir, tambi\u00e9n tiene forma de campana. En este tutorial voy a explicar c\u00f3mo trabajar con la distribuci\u00f3n t de Student en R usando las funciones dt(), qt(), pt() y rt(). Es decir, la funci\u00f3n de densidad, la acumulada, la funci\u00f3n cuantil y como generar n\u00fameros aleatorios<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"ast-oembed-container \" style=\"height: 100%;\"><iframe loading=\"lazy\" title=\"Distribuci\u00f3n T de STUDENT en Rstudio\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/oGiQHcp6C0U?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/div>\n<\/div><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>C\u00d3DIGO EN R DEL VIDEO\n\n#DISTRIBUCION T STUDENT EN R\r\n\r\n\r\n\r\n# funciones que usaremos \r\n\r\n?dt\r\n\r\n#dt  -  densidad\r\n#pt  -  distribution acumulada\r\n#qt  -  quantile function\r\n#rt  - generador de numeros aleatorios\r\n\r\n\r\n# ejemplos\r\n\r\n#encontrar el valor de la distribuci\u00f3n t de Student (pdf )\r\n#en x = 0 con 10 grados de libertad\r\n\r\ndt(x=0, df= 10)\r\n\r\ndt(0,10)\r\n\r\n\r\n#encontrar el valor de la distribuci\u00f3n t de Student pdf \r\n#en x = 2 con 15 grados de libertad\r\n\r\ndt(2,15)\r\n\r\n# grafico con dt\r\n\r\n\r\n\r\n#1 creamos una secuencia de 100 n\u00fameros entre -4 y 4\r\n\r\nx &lt;- seq(-4, 4, length=100)\r\n\r\n#2. crear un vector de valores que muestre la altura de la distribuci\u00f3n de probabilidad\r\n#para cada valor en x, usando 20 grados de libertad\r\n\r\ny &lt;- dt(x = x, df = 20)\r\n\r\n#Grafico y a\u00f1adimos los valores\r\n\r\nplot(x,y, type = \"l\", lwd = 2, axes = FALSE, xlab = \"Victor A.Rico\", ylab = \"\",main=\"Distribuci\u00f3n t_student\")\r\naxis(1, at = -3:3, labels = c(\"-3s\", \"-2s\", \"-1s\", \"Media\", \"1s\", \"2s\", \"3s\"))\r\n\r\n\r\n# Funci\u00f3n de densidad acumulada (cdf) --\r\n\r\npt(x,df)   # por defecto devuelve el area a la izquierda de la distribucion\r\n           # P&#91;X \u2264 x]\r\n\r\n# is quieres medir el lado derecho puedes poner \r\n\r\npt(x, df, lower.tail = FALSE) \r\n\r\n\r\n\r\n\r\n#cual es la probabilidad de que una variable t de Student de 6 grados de libertad \r\n#deja a la izquierda de -1,45:\r\n\r\n# P&#91;t6 \u2264 -1.45]\r\n\r\npt(-1.45,6)\r\n\r\n#\u2660Cual es la probabilidad acumulada a la derecha de 2,45, \r\n#en una variable t de Student de 15 grados de libertad\r\n\r\n#P&#91;t15 >= 2.45]\r\n\r\npt(2.45,15) # P &#91;t15&lt;2.45]\r\n\r\n1-pt(2.45,15)\r\n\r\n\r\n#P(t9 > -1.95)\r\n\r\npt(-1.95,9)\r\n\r\n1-pt(-1.95,9)\r\n\r\n1-0.04148336\r\n\r\n#Cual es la probabilidad acumulada de una variable t de Student de 25 grados de libertad, \r\n#se encuentre entre: 0,75 y 1,25\r\n\r\n#P(0.75 &lt; t25 &lt; 1.25) =\r\n\r\n#P (t25&lt;1.25) - P(t25&lt; 0.75)\r\n\r\npt(1.25,25)- pt(0.75,25)\r\n\r\n\r\n## Funci\u00f3n CUARTIL \r\n\r\n# Ser\u00e1 la inversa de la funci\u00f3n de densidad acumulada\r\n\r\n\r\n#Encuentra el valor t del cuantil 95 de la distribuci\u00f3n t de Student con df = 20\r\n\r\nqt(0.95,20)\r\n\r\npt(1.724718,20) #comprobaci\u00f3n con pt\r\n\r\n\r\nqt(0.1,20)\r\n\r\npt(-1.325341,20)\r\n\r\n\r\n## N\u00fameros aleatorios\r\n\r\n#generar un vector de 1000 variables aleatorias con dist t y 15 grados libertad\r\n\r\nt_aleatorio&lt;- rt(1000,15)\r\n\r\nplot(t_aleatorio)\r\n\r\nhist(t_aleatorio)\r\n\r\n\r\nt_aleatorio &lt;- rt(1000,500)\r\n\r\nplot(t_aleatorio)\r\n\r\nhist(t_aleatorio)<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>En probabilidad y estad\u00edstica, la distribuci\u00f3n T de Student es una distribuci\u00f3n de probabilidad que surge del problema de estimar la media de una poblaci\u00f3n normalmente distribuida cuando el tama\u00f1o de la muestra es peque\u00f1o y la desviaci\u00f3n est\u00e1ndar poblacional es desconocida. La representaci\u00f3n gr\u00e1fica se parece a la distribuci\u00f3n normal, es decir, tambi\u00e9n tiene &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/ricovictor.com\/index.php\/2022\/04\/16\/distribucion-t-de-student-en-rstudio\/\"> <span class=\"screen-reader-text\">Distribuci\u00f3n T de STUDENT en Rstudio<\/span> Leer m\u00e1s &raquo;<\/a><\/p>\n","protected":false},"author":19,"featured_media":3173,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[2],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Distribuci\u00f3n T de STUDENT en Rstudio - V\u00edctor A. Rico \u2014 Econometr\u00eda y Finanzas Cuantitativas<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ricovictor.com\/index.php\/2022\/04\/16\/distribucion-t-de-student-en-rstudio\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Distribuci\u00f3n T de STUDENT en Rstudio - V\u00edctor A. Rico \u2014 Econometr\u00eda y Finanzas Cuantitativas\" \/>\n<meta property=\"og:description\" content=\"En probabilidad y estad\u00edstica, la distribuci\u00f3n T de Student es una distribuci\u00f3n de probabilidad que surge del problema de estimar la media de una poblaci\u00f3n normalmente distribuida cuando el tama\u00f1o de la muestra es peque\u00f1o y la desviaci\u00f3n est\u00e1ndar poblacional es desconocida. 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