{"id":6530,"date":"2025-07-15T13:34:48","date_gmt":"2025-07-15T13:34:48","guid":{"rendered":"https:\/\/functiontranslator.com\/loi-exponentielle-n\/"},"modified":"2021-02-26T08:05:57","modified_gmt":"2021-02-26T08:05:57","slug":"expon-dist","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/fr\/expon-dist\/","title":{"rendered":"LOI.EXPONENTIELLE.N"},"content":{"rendered":"

Description de la fonction<\/h2>\n

La fonction EXPON.DIST<\/strong> dans MS Excel et LOI.EXPONENTIELLE.N<\/strong> dans Google Sheets est utilis\u00e9e pour calculer la probabilit\u00e9 qu’une variable al\u00e9atoire suivant une distribution exponentielle prenne une valeur d\u00e9termin\u00e9e. Cette distribution continue est fr\u00e9quemment employ\u00e9e pour mod\u00e9liser le temps \u00e9coul\u00e9 entre des \u00e9v\u00e9nements successifs et ind\u00e9pendants, survenant \u00e0 un rythme constant.<\/p>\n

Syntaxe<\/h2>\n

Dans MS Excel, la syntaxe est : <\/p>\n

=EXPON.DIST(x, lambda, cumulatif)<\/code><\/pre>\n
 Dans Google Sheets, elle est pr\u00e9sent\u00e9e en fran\u00e7ais : <\/p>\n
=LOI.EXPONENTIELLE.N(x, lambda, cumulatif)<\/code><\/pre>\n
 O\u00f9 : <\/p>\n
    \n
  • x<\/strong> : la valeur \u00e0 laquelle la fonction est \u00e9valu\u00e9e.<\/li>\n
  • lambda<\/strong> : le taux moyen des \u00e9v\u00e9nements, doit \u00eatre un nombre positif.<\/li>\n
  • cumulatif<\/strong> : un param\u00e8tre bool\u00e9en qui indique le type de r\u00e9sultat souhait\u00e9. Si vrai, la fonction retourne la distribution cumul\u00e9e; si faux, elle retourne la densit\u00e9 de probabilit\u00e9.<\/li>\n<\/ul>\n
    Exemples d’utilisation<\/h2>\n\n\n\n\n
    Formule<\/th>\nDescription<\/th>\nR\u00e9sultat<\/th>\n<\/tr>\n
    =EXPON.DIST(1, 0.5, FAUX)<\/code><\/td>\nCalcule la densit\u00e9 de probabilit\u00e9 pour x=1 avec un lambda de 0.5.<\/td>\nEnviron 0.303<\/td>\n<\/tr>\n
    =EXPON.DIST(1, 0.5, VRAI)<\/code><\/td>\nCalcule la distribution cumul\u00e9e pour x=1 avec un lambda de 0.5.<\/td>\nEnviron 0.393<\/td>\n<\/tr>\n<\/table>\n
    Exercice pratique 1 : Calcul du temps moyen d’attente<\/h2>\n
    Prenons l’exemple d’un centre d’appels o\u00f9 les appels arrivent en moyenne toutes les 20 minutes. Nous souhaitons \u00e9valuer la probabilit\u00e9 qu’un client n’attende pas plus de 10 minutes.<\/p>\n
    Solution :<\/strong><\/p>\n
     =EXPON.DIST(10, 1\/20, VRAI) <\/code><\/pre>\n
    Les param\u00e8tres ici sont ‘x’ \u00e9gal \u00e0 10 minutes et ‘lambda’ de 1\/20, repr\u00e9sentant un appel toutes les 20 minutes. Cela nous permet de trouver la probabilit\u00e9 cumul\u00e9e qu’un appel arrive dans les 10 minutes suivant le dernier appel.<\/p>\n
    Exercice pratique 2 : \u00c9valuation de la fiabilit\u00e9 d’un \u00e9quipement<\/h2>\n
    Si un \u00e9quipement pr\u00e9sente un taux de panne suivant une distribution exponentielle avec un lambda de 0.03, quelle est la probabilit\u00e9 que cet \u00e9quipement fonctionne sans faille pendant au moins 50 heures ?<\/p>\n
    Solution :<\/strong><\/p>\n
     =1 - EXPON.DIST(50, 0.03, VRAI) <\/code><\/pre>\n
    Ce calcul nous donne la probabilit\u00e9 que l’\u00e9quipement continue de fonctionner sans d\u00e9faillance pendant au moins 50 heures en utilisant l’inverse de la fonction de distribution cumul\u00e9e.<\/p>\n
     Ce texte reformul\u00e9 explique clairement et professionnellement comment appliquer la fonction EXPON.DIST en contexte r\u00e9el pour des analyses de donn\u00e9es ou des pr\u00e9visions statistiques.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Renvoie la distRibution exponentielle<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[315],"tags":[],"class_list":["post-6530","post","type-post","status-publish","format-standard","hentry","category-statistiques"],"acf":[],"yoast_head":"\nFonction EXPON.DIST (LOI.EXPONENTIELLE.N) dans Excel : comment \u00e7a marche, exemples et syntaxe<\/title>\n<meta name=\"description\" content=\"Pr\u00e9sentation de la fonction EXPON.DIST (LOI.EXPONENTIELLE.N) d\u2019Excel et Google Sheets. 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