{"id":3334,"date":"2022-08-09T13:44:48","date_gmt":"2022-08-09T13:44:48","guid":{"rendered":"https:\/\/ricovictor.com\/?p=3334"},"modified":"2026-01-25T17:25:32","modified_gmt":"2026-01-25T17:25:32","slug":"distribucion-gamma-en-rstudio","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2022\/08\/09\/distribucion-gamma-en-rstudio\/","title":{"rendered":"Distribuci\u00f3n GAMMA en Rstudio"},"content":{"rendered":"\n<p>En probabilidad la <strong>Distribuci\u00f3n Gamma<\/strong> se utiliza com\u00fanmente en estudios de supervivencia de fiabilidad o para modelar las probabilidades relacionadas con los tiempos de espera. Por ejemplo, la distribuci\u00f3n gamma puede describir el tiempo que transcurre para que falle un componente el\u00e9ctrico. <\/p>\n\n\n\n<p>Hay que tener en cuenta que ser\u00e1 usada para modelar valores de datos que sean ASIM\u00c9TRICOS hacia la derecha y mayores que 0. Estar\u00e1 formada por 2 par\u00e1metros que son la Forma y la Escala. Aqu\u00ed te explico un poco sobre esta distribuci\u00f3n y muestro las funciones que puedes usar en R para trabajar con ella. <\/p>\n\n\n\n<p>M\u00e1s abajo tienes el c\u00f3digo R del tutorial <\/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 GAMMA | Explicaci\u00f3n y ejemplo en Rstudio\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/cmUByPPZdKQ?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/div>\n<\/div><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>CODIGO R DEL TUTORIAL \n\n#DISTRIBUCION GAMMA\r\n\r\n\r\n\r\n#Usaremos las siguientes funciones para trabajar con la distribucion gamma en R\r\n\r\n#shape = forma  rate = lamda o beta inversa   scale = 1\/rate\r\n\r\n#shape = alfa #scale = Beta # lambda o  b-1 = 1\/beta\r\n\r\n\r\n\r\ndgamma(x, shape, rate,scale) # funci\u00f3n de densidad con una determinada escala y forma\r\n\r\npgamma(q, shape, rate,scale) #funci\u00f3n de distribucion acumulada\r\n\r\nqgamma(p, shape, rate,scale) #funcion inversa o cuantil\r\n\r\nrgamma(n, shape, rate,scale) #numero aleatorios en base a gamma\r\n\r\n#####################################3\r\n?dgamma\r\n\r\n# How to Use rgamma()\r\n\r\n# Semilla para que salgan los mismo valores\r\n\r\nset.seed(0)\r\n\r\n#Generamos una muestra de 1000 n\u00fameros aleatorios en base a distribuci\u00f3n GAMMA\r\n\r\nx &lt;- rgamma(n=1000, shape=5, scale=1\/3)\r\n\r\n#CREAMOS UN HISTOGRAMA\r\nhist(x)\r\n\r\n\r\nset.seed(0)\r\nx &lt;- rgamma(n=1000, shape=5, rate=3)\r\n\r\nhist(x)\r\n\r\n\r\n# GR\u00c1FICO DISTRIBUCION GAMMA EN R\r\n\r\nx = 0:10\r\ncurve(dgamma(x, 2, scale=1), xlab = \"x\", ylab = \"f(x;a,\u00df)\", 0, 10, col = 3, lwd = 3, \r\n      main = \"Gr\u00e1fico distribuci\u00f3n Gamma\")\r\ncurve(dgamma(x, 1, scale=0.5), xlab = \"x\", ylab = \"f(x;a,\u00df)\", 0, 10, col = 5, lwd = 3, \r\n      add = TRUE)\r\ncurve(dgamma(x, 11, scale=0.25), xlab = \"x\", ylab = \"f(x;a,\u00df)\", 0, 10, col = 7, lwd = 3, \r\n      add = TRUE)\r\nlegend(\"topright\", c(\"a=2,\u00df=1\", \"a=1,\u00df=0.5\", \"a=11,\u00df=0.25\"), col = c(3, 5, 7), lwd = 3, \r\n       inset = 0.05)\r\n\r\n\r\n#\r\ncurve(dgamma(x, 2, 1), xlab = \"x\", ylab = \"f(x;a,\u00df)\", 0, 10, col = 4, lwd = 3, \r\n      main = \"Distribuci\u00f3n Gamma (a=2,\u00df=1)\")\r\n\r\ncurve(pgamma(x, 2, 1), xlab = \"x\", ylab = \"f(x;a,\u00df)\", 0, 10, col = 4, lwd = 3, \r\n      main = \" Funci\u00f3n de Distribuci\u00f3n Acumulada Gamma (a=2,\u00df=1)\")\r\n\r\n#### \r\n\r\n#Ejemplo: Suponga que el tiempo, en\r\n#horas, que toma reparar una bomba es una variable aleatoria x que\r\n#tiene una distribuci\u00f3n gamma con par\u00e1metros a = 2 y\r\n#b= 1\/2. \u00bfCu\u00e1l es la probabilidad de que en el\r\n#siguiente servicio:\r\n  \r\n  #a) tome cuando mucho 1 hora  reparar la bomba?\r\n  # P(X&lt;=1)\r\n \r\n #el propio ejercicio nos da a = 2 y b(escala)= 1\/2\r\n\r\n pgamma(1, shape=2, scale=1\/2) \r\n \r\n \r\n pgamma(1, shape=2, rate=2) \r\n \r\n  \r\n \r\n  #b) Al menos se requieren 2 horas para reparar la bomba?\r\n  # P (X>=2) \u00f3\r\n  # 1 - P(X&lt;=2)\r\n \r\n  pgamma(2, shape=2, scale=1\/2)  # P(X&lt;=2)\r\n  \r\n  1- 0.9084218 \r\n  \r\n  1-pgamma(2, shape=2, scale=1\/2)\r\n\r\n  #c) que tarde entre 2 y 1\r\n  \r\n  P(1 &lt; X &lt; 2)\r\n  \r\n  pgamma(2, shape=2, scale=1\/2) - pgamma(1, shape=2, scale=1\/2)\r\n\r\n  \r\n  # Funcion inversa.. Si nos dan la probabilidad en vez de q\r\n  \r\n  #^\u00bfcuanto tiempo como mucho tardar\u00e1 en reparar la bomba para una probabilidad\r\n  #acumulada de 0.5940\r\n  \r\n  #p=0.5939942\r\n  \r\n   qgamma(0.5939942, shape=2, scale=1\/2)\r\n   \r\n   \r\n   #Si la probabilidad es de 0.09157 cuantas horas al menos se requieren?\r\n   \r\n   1 - 0.09157\r\n   \r\n   qgamma(0.90843, shape=2, scale=1\/2)\r\n   \r\n   \r\n   \r\n   \r\n   \r\n #EJEMPLO 2\r\n   \r\n#En una ciudad el consumo de energ\u00eda diario en millones de kilovatios hora\r\n   #puede considerarse como una variable con distribucion gamma \r\n   #de parametros a=3 b-1= 0.5\r\n   \r\n   #\u00bfQu\u00e9 probabilidad hay de que se consuma entre 3 y 8 mill de Kw\/hora\r\n   \r\n   #P(3&lt; X &lt; 8)\r\n   \r\n    #aqu\u00ed para sacar la escala tenemos que hacer  1\/0.5\r\n    \r\n    \r\n    \r\n   \r\n    \r\n   pgamma(8, shape=3, scale =2)-pgamma(3, shape=3, scale=2) \r\n    \r\n   #b) si la planta cap 10 m \/h .. \u00bfprob de que en un d\u00eda sea insuficiente?\r\n    \r\n   P(X>10)\r\n    \r\n   1-pgamma(10, shape=3, scale=2) \r\n    \r\n    \r\n   1- pgamma(10, shape=3, rate=1\/2) \r\n    \r\n    \r\n    \r\n  #################################################################### <\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>En probabilidad la Distribuci\u00f3n Gamma se utiliza com\u00fanmente en estudios de supervivencia de fiabilidad o para modelar las probabilidades relacionadas con los tiempos de espera. Por ejemplo, la distribuci\u00f3n gamma puede describir el tiempo que transcurre para que falle un componente el\u00e9ctrico. Hay que tener en cuenta que ser\u00e1 usada para modelar valores de datos &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/ricovictor.com\/index.php\/2022\/08\/09\/distribucion-gamma-en-rstudio\/\"> <span class=\"screen-reader-text\">Distribuci\u00f3n GAMMA en Rstudio<\/span> Leer m\u00e1s &raquo;<\/a><\/p>\n","protected":false},"author":19,"featured_media":3336,"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 GAMMA en Rstudio - V\u00edctor A. 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