{"id":2208,"date":"2021-03-21T23:36:40","date_gmt":"2021-03-21T23:36:40","guid":{"rendered":"https:\/\/ricovictor.com\/?p=2208"},"modified":"2026-01-29T21:52:41","modified_gmt":"2026-01-29T21:52:41","slug":"distribucion-de-poisson-en-r","status":"publish","type":"post","link":"https:\/\/ricovictor.com\/index.php\/2021\/03\/21\/distribucion-de-poisson-en-r\/","title":{"rendered":"Distribuci\u00f3n de Poisson en R"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"2208\" class=\"elementor elementor-2208\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-741f3ef9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"741f3ef9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-57404f2a\" data-id=\"57404f2a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5a55527f elementor-widget elementor-widget-text-editor\" data-id=\"5a55527f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p class=\"_04xlpA direction-ltr align-center para-style-body\"><span class=\"JsGRdQ\"><strong>La Distribuci\u00f3n de Poisson<\/strong> es una distribuci\u00f3n de <\/span><span class=\"JsGRdQ\">probabilidad discreta <\/span><span class=\"JsGRdQ\">usada para determinar la probabilidad de que ocurra un determinado n\u00famero de eventos <\/span><span class=\"JsGRdQ\">durante cierto per\u00edodo de tiempo<\/span><\/p><p class=\"_04xlpA direction-ltr align-center para-style-body\"><span class=\"JsGRdQ\">Est\u00e1 definida con un \u00fanico par\u00e1metro, que suele notarse por<strong> \u03bb(Lambda)<\/strong>. Normalmente este<\/span> <span class=\"JsGRdQ\">par\u00e1metro \u03bb representa el n\u00famero medio de sucesos que ocurren por unidad de tiempo. De forma que definiremos la variable aleatoria X y su distribuci\u00f3n como sigue:<\/span><\/p><ul><li class=\"_04xlpA direction-ltr align-center para-style-body\"><span class=\"JsGRdQ\">Variable aleatoria<\/span> <span class=\"JsGRdQ\">X = \u201cN\u00famero de sucesos aleatorios que ocurren en un<\/span><span class=\"JsGRdQ\">determinado periodo de tiempo\u201d<\/span><\/li><\/ul><ul><li class=\"_04xlpA direction-ltr align-center para-style-body\"><span class=\"JsGRdQ\">Distribuci\u00f3n, X \u2192 P(\u03bb)<\/span><\/li><\/ul><p>Esta distribuci\u00f3n se puede usar de manera muy com\u00fan y hay muchos ejemplos como :<\/p><p class=\"_04xlpA direction-ltr align-start para-style-body\"><span class=\"JsGRdQ\">*N\u00famero de defectos de una tela por m2<\/span><\/p><p class=\"_04xlpA direction-ltr align-start para-style-body\">\u00a0<\/p><p class=\"_04xlpA direction-ltr align-start para-style-body\"><span class=\"JsGRdQ\">*N\u00famero de clientes que llegan a un determinado establecimiento en un per\u00edodo de tiempo dado<\/span><\/p><p class=\"_04xlpA direction-ltr align-start para-style-body\">\u00a0<\/p><p class=\"_04xlpA direction-ltr align-start para-style-body\"><span class=\"JsGRdQ\">*N\u00famero de llegadas de embarcaciones a un puerto por d\u00eda, mes, etc.<\/span><\/p><p class=\"_04xlpA direction-ltr align-start para-style-body\">\u00a0<\/p><p class=\"_04xlpA direction-ltr align-start para-style-body\"><span class=\"JsGRdQ\">*N\u00famero de goles que un equipo convierte por partido<\/span><\/p><p>&#8230;..<\/p><p>Para profundizar m\u00e1s en el estudio de esto he creado un tutorial con ejemplos pr\u00e1cticos usando R. M\u00e1s abajo los tienes, y tambi\u00e9n el c\u00f3digo usado por si quieres copiarlo.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7d1bff8 elementor-view-stacked elementor-shape-circle elementor-widget elementor-widget-icon\" data-id=\"7d1bff8\" data-element_type=\"widget\" data-widget_type=\"icon.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-wrapper\">\n\t\t\t<div class=\"elementor-icon\">\n\t\t\t<i aria-hidden=\"true\" class=\"far fa-hand-point-down\"><\/i>\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6534e41 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6534e41\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-667be1ce\" data-id=\"667be1ce\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-42885863 elementor-widget elementor-widget-video\" data-id=\"42885863\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=LGvuJg83B0Q&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5cef113f elementor-widget elementor-widget-spacer\" data-id=\"5cef113f\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3e66cbe elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3e66cbe\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8c7d490\" data-id=\"8c7d490\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-56d200b2 elementor-view-stacked elementor-shape-circle elementor-widget elementor-widget-icon\" data-id=\"56d200b2\" data-element_type=\"widget\" data-widget_type=\"icon.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-wrapper\">\n\t\t\t<div class=\"elementor-icon\">\n\t\t\t<i aria-hidden=\"true\" class=\"fas fa-arrow-circle-down\"><\/i>\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-15825a61 elementor-drop-cap-yes elementor-drop-cap-view-default elementor-widget elementor-widget-text-editor\" data-id=\"15825a61\" data-element_type=\"widget\" data-settings=\"{&quot;drop_cap&quot;:&quot;yes&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<h2>Codigo R<\/h2><p>\u00a0<\/p><p>## Funci\u00f3n masa de probabilidad<\/p><p>dpois(x, lambda)<\/p><p># Funci\u00f3n de ditribuci\u00f3n<\/p><p>ppois(q, lambda)<\/p><p>#Cuantiles<\/p><p>qpois(p, lambda)<\/p><p># N\u00fameros aleatorios<\/p><p>rpois(n, lambda)<\/p><p>################<\/p><p>## 100 horas &#8212; Promedio 8<\/p><p># Definimos nuestra variable aleatoria &#8212; \u03bb = [X] = 8,<\/p><p><br \/># falle 1 en 25 hora<\/p><p>100\/25<\/p><p>8\/4<\/p><p>dpois(x, lambda)<\/p><p>dpois(1, 2)<\/p><p>0.2706706<\/p><p># fallen no m\u00e1s de 2 en 50 horas<\/p><p>100\/50<\/p><p>8\/2<\/p><p>#P(0)+P(1)+P(2)<br \/>dpois(0, 4)+ dpois(1, 4) +dpois(2, 4)<br \/>0.2381033<\/p><p>#P( X&lt;=2)<\/p><p>ppois(2, 4)<\/p><p># fallen al menos 10 en 125 horas<\/p><p>100\/125<\/p><p>8\/0.8<\/p><p>#P X&gt;=10<br \/># = 1 &#8211; P( X&lt;10)<\/p><p><br \/>1- ppois(9,10)<\/p><p>0.5420703<\/p><p>###################<\/p><p>#El n\u00famero medio de enfermos recibidos cada 10 minutos en un <br \/>#centro sanitario entre las 10 horas y las 15 horas es 1.8. <br \/>#Suponiendo que dicho n\u00famero de enfermos sigue una distribuci\u00f3n de Poisson. Se pide:<\/p><p>#Calcular la probabilidad de que entre las 12 horas y las 12 horas y 10 minutos haya:<\/p><p>#definimos variable y distribuci\u00f3n<\/p><p>#x= N\u00daMERO DE ENFERMOS RECIBIDOS EN 10 MINUTOS<br \/>#LMABDA= 1.8<\/p><p>#1) Ning\u00fan enfermo<\/p><p>dpois(0, 1.8)<\/p><p>#2) Exactamente 2 enfermos P[X = 2]<\/p><p>dpois(2, 1.8)<\/p><p>#3) M\u00e1s de 8 enfermos P[X \u2265 9]<\/p><p># = 1 \u2013 P[X \u2264 8]<\/p><p>ppois(8,1.8)<\/p><p>1-0.9998903<\/p><p>1- ppois(8, 1.8)<\/p><p><br \/>#4) Entre 8 y 15 clientes (ambos inclusive) P[8 \u2264 X \u2264 15]<\/p><p>#= P[X \u2264 15] \u2013 P[ X \u2264 7]<\/p><p>ppois(c(15, 7), 1.8)<\/p><p>1.0000000 &#8211; 0.9994385<\/p><p>#separado<\/p><p>ppois(15, 1.8)<br \/>ppois(7, 1.8)<\/p><p><br \/>#6) Generar una muestra de 20 valores aleatorios de la distribuci\u00f3n.<\/p><p>r_p&lt;- rpois(20, 1.8)<\/p><p>hist(r_p)<\/p><p>#####<\/p><p># Ejemplo goles<\/p><p># Saber la probabilidad de que el partido Real madrid vs Osasuna sea 2-1<\/p><p># Media de goles en liga del Madrid 2.5 &#8211; <br \/># media del Osasuna 1.8<\/p><p>P_madrid&lt;- dpois(2,2.5) # P X =2 Real Madrid<\/p><p>P_Osasuna&lt;- dpois(1,1.8) ## P X = 1 Osasuna<\/p><p>P_madrid * P_Osasuna<\/p><p><br \/>ppois(3,2.5) #P x&lt;=3<\/p><p>## probabilidades de goles conjuntos, tambi\u00e9n varios resultados&#8230;<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>La Distribuci\u00f3n de Poisson es una distribuci\u00f3n de probabilidad discreta usada para determinar la probabilidad de que ocurra un determinado n\u00famero de eventos durante cierto per\u00edodo de tiempo Est\u00e1 definida con un \u00fanico par\u00e1metro, que suele notarse por \u03bb(Lambda). Normalmente este par\u00e1metro \u03bb representa el n\u00famero medio de sucesos que ocurren por unidad de tiempo. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/ricovictor.com\/index.php\/2021\/03\/21\/distribucion-de-poisson-en-r\/\"> <span class=\"screen-reader-text\">Distribuci\u00f3n de Poisson en R<\/span> Leer m\u00e1s &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":2212,"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 de Poisson en R - V\u00edctor A. 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