{"id":306,"date":"2014-10-16T00:25:23","date_gmt":"2014-10-15T22:25:23","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/intervalle-de-fluctuation-dune-loi-binomiale-avec-r\/"},"modified":"2023-10-14T20:14:32","modified_gmt":"2023-10-14T18:14:32","slug":"intervalle-de-fluctuation-dune-loi-binomiale-avec-r","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/la-loi-binomiale-avec-r\/intervalle-de-fluctuation-dune-loi-binomiale-avec-r\/","title":{"rendered":"Intervalle de fluctuation d&rsquo;une loi binomiale avec R"},"content":{"rendered":"<h2>Pr\u00e9sentation<\/h2>\n<p>Soit X une variable al\u00e9atoire suivant une loi binomiale de param\u00e8tres<\/p>\n<p>$(n ; p)$.<\/p>\n<p>On cherche l&rsquo;intervalle de fluctuation au seuil de 95%.<\/p>\n<p>En d\u00e9but de script, on fixe les param\u00e8tres.<\/p>\n<p>En sortie, on obtient :<br \/>\n&#8211; le d\u00e9tail pour l&rsquo;obtention de $a$ et $b$ ;<br \/>\n&#8211; l&rsquo;intervalle <span class=\"katex-eq\" data-katex-display=\"false\"> \\left[ \\frac{a}{n} ; \\frac{b}{n}\\right]<\/span>&nbsp;;<br \/>\n&#8211; les diagrammes en b\u00e2tons associ\u00e9s.<\/p>\n<h2>Le script<\/h2>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">#------------------------------------ A modifier\nn&lt;-20\np&lt;-0.4\n\n\n#-----------------------------------------------\n# Calcul de a\n\ni&lt;-0\nsommeProba&lt;-pbinom(q=i,size=n,prob=p)\n\nwhile (sommeProba&lt;=0.025)\n{\n  i&lt;-i+1\n  sommeProba&lt;-pbinom(q=i,size=n,prob=p)\n}\na&lt;-i\n \ntexte&lt;-paste(\"p(X &lt;=\", bquote( .(a-1)),  \") = \", bquote( .(pbinom(q=a-1,size=n,prob=p))))\nprint(texte)\ntexte&lt;-paste(\"p(X &lt;=\", bquote( .(a)),   \") = \", bquote( .(pbinom(q=a,size=n,prob=p))))\nprint(texte)\ntexte&lt;-paste(\"a = \", bquote( .(a)))\nprint(texte)\n\n#-------------------------------------------------\n# Calcul de b\n\ni&lt;-0\nsommeProba&lt;-pbinom(q=i,size=n,prob=p)\n\nwhile (sommeProba&lt;0.975)\n{\n  i&lt;-i+1\n  sommeProba&lt;-pbinom(q=i,size=n,prob=p)\n}\nb&lt;-i\ntexte&lt;-paste(\"p(X &lt;=\", bquote( .(b-1)),   \") = \", bquote( .(pbinom(q=b-1,size=n,prob=p))))\nprint(texte)\ntexte&lt;-paste(\"p(X &lt;=\", bquote( .(b)),   \") = \", bquote( .(pbinom(q=b,size=n,prob=p))))\nprint(texte)\ntexte&lt;-paste(\"b = \", bquote( .(b)))\nprint(texte)\n\n#-----------------------------------------------\n# Calcul de l'intervalle de fluctuation\n\nprint(\"Intervalle de fluctuation au seuil de 95%\")\n\ntexte&lt;-paste(\"a\/n = \", bquote( .(a\/n)))\nprint(texte)\ntexte&lt;-paste(\"b\/n = \", bquote( .(b\/n)))\nprint(texte)\n\n\n# Cr\u00e9ation du tableau des densit\u00e9s\n\nx&lt;-0:n\n\ntabDensite&lt;-NULL\nfor (i in x)  {tabDensite&lt;-c(tabDensite,dbinom(i,n,p))}\n\n# Creation des textes\n\n\ntexteTitre&lt;-paste(\"Loi binomiale\", \"\\n\"\n                  , \"n = \", bquote( .(n)),\"\\n\"\n                  , \"p = \", bquote( .(p)),\"\\n\"\n                  \n                  )\n\n\n# Cr\u00e9ation du diagramme en b\u00e2tons des densit\u00e9s\n\n\nbp&lt;-barplot(rbind(tabDensite),beside=TRUE,las=1,names.arg=x,\n        col=c(rep(\"red\",a),rep(\"blue\",b-a+1),rep(\"red\",n-b))\n        ,ylim=c(0,0.25)\n        ,xlab=\"k\",ylab=\"P(X = k)\",main=texteTitre,cex.main=0.8)\n\ntexte.a&lt;-paste(\"a = \", bquote( .(a)))\ntext(x=bp[a+1],y=0.2,texte.a,pos=2)\n\n\ntexte&lt;-bquote( .(round(sum(dbinom(0:(a-1),n,p)),digits=3)))\ntext(x=bp[a+1],y=0.23,texte,pos=2,col=\"red\")\n\ntexte.b&lt;-paste(\"b = \", bquote( .(b)))\ntext(x=bp[b+1],y=0.2,texte.b,pos=4)\n\n\ntexte&lt;-bquote( .(round(sum(dbinom((b+1):n,n,p)),digits=3)))\ntext(x=bp[b+1],y=0.23,texte,pos=4,col=\"red\")\n\n\ntexte&lt;-bquote( .(round(sum(dbinom(a:b,n,p)),digits=3)))\ntext(x=bp[round((a+b)\/2)],y=0.23,texte,col=\"blue\")\n\nsegments(bp[a+1],0,bp[a+1],0.25,lty=2)\nsegments(bp[b+1],0,bp[b+1],0.25,lty=2)\n\n\n# Cr\u00e9ation du tableau des densit\u00e9s cumul\u00e9s\n\ntabDensitesCumulees&lt;-NULL\nfor (i in x)  {tabDensitesCumulees&lt;-c(tabDensitesCumulees,pbinom(i,n,p))}\n\n# Cr\u00e9ation du diagramme en b\u00e2tons des densit\u00e9es cumul\u00e9es\n\n\nbp&lt;-barplot(rbind(tabDensitesCumulees),beside=TRUE,las=1,names.arg=x,\n            col=c(rep(\"red\",a),rep(\"blue\",b-a+1),rep(\"red\",n-b))\n            ,ylim=c(0,1)\n            ,xlab=\"k\",ylab=\"P(X &lt;= k)\",main=texteTitre,cex.main=0.8)\n\n#texte.a&lt;-bquote( .(round(sum(dbinom(a:b,n,p)),digits=3)))\n#text(bp[round((a+b)\/2)],y=0.9,texte.a,col=\"blue\")\n\nsegments(bp[a+1],0,bp[a+1],1,lty=2)\nsegments(bp[b+1],0,bp[b+1],1,lty=2)\n\nsegments(bp[1],0.025,bp[n+1],0.025,lty=2)\nsegments(bp[1],0.975,bp[n+1],0.975,lty=2)<\/pre>\n<p>Dans la console, on obtient :<\/p>\n<p><code><br \/>\n[1] \"p(X &lt;= 3 ) =  0.0159611627900082\"<br \/>\n[1] \"p(X &lt;= 4 ) =  0.0509519531941666\"<br \/>\n[1] \"a =  4\"<br \/>\n[1] \"p(X &lt;= 11 ) =  0.943473632965747\"<br \/>\n[1] \"p(X &lt;= 12 ) =  0.978971072522229\"<br \/>\n[1] \"b =  12\"<br \/>\n[1] \"Intervalle de fluctuation au seuil de 95%\"<br \/>\n[1] \"a\/n =  0.2\"<br \/>\n[1] \"b\/n =  0.6\"<br \/>\n<\/code><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-922\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_loi_binomiale_05.png\" alt=\"loi_binomiale_05.png\" width=\"579\" height=\"360\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_loi_binomiale_05.png 579w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_loi_binomiale_05-300x187.png 300w\" sizes=\"auto, (max-width: 579px) 100vw, 579px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-923\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_loi_binomiale_06.png\" alt=\"loi_binomiale_06.png\" width=\"579\" height=\"360\" align=\"center\" srcset=\"https:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_loi_binomiale_06.png 579w, https:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_loi_binomiale_06-300x187.png 300w\" sizes=\"auto, (max-width: 579px) 100vw, 579px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pr\u00e9sentation Soit X une variable al\u00e9atoire suivant une loi binomiale de param\u00e8tres $(n ; p)$. On cherche l&rsquo;intervalle de fluctuation au seuil de 95%. En d\u00e9but de script, on fixe&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2083,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-306","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Intervalle de fluctuation d&#039;une loi binomiale avec R - Maths &amp; Num\u00e9rique<\/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:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/la-loi-binomiale-avec-r\/intervalle-de-fluctuation-dune-loi-binomiale-avec-r\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Intervalle de fluctuation d&#039;une loi binomiale avec R - Maths &amp; Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Pr\u00e9sentation Soit X une variable al\u00e9atoire suivant une loi binomiale de param\u00e8tres $(n ; p)$. On cherche l&rsquo;intervalle de fluctuation au seuil de 95%. En d\u00e9but de script, on fixe&hellip;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/la-loi-binomiale-avec-r\/intervalle-de-fluctuation-dune-loi-binomiale-avec-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Maths &amp; Num\u00e9rique\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-14T18:14:32+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2014\/10\/png_loi_binomiale_05.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/la-loi-binomiale-avec-r\/intervalle-de-fluctuation-dune-loi-binomiale-avec-r\/\",\"url\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/la-loi-binomiale-avec-r\/intervalle-de-fluctuation-dune-loi-binomiale-avec-r\/\",\"name\":\"Intervalle de fluctuation d'une loi binomiale avec R - Maths &amp; 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