{"id":6563,"date":"2025-07-15T13:34:48","date_gmt":"2025-07-15T13:34:48","guid":{"rendered":"https:\/\/functiontranslator.com\/loi-gamma-n\/"},"modified":"2021-02-26T08:06:52","modified_gmt":"2021-02-26T08:06:52","slug":"gamma-dist","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/fr\/gamma-dist\/","title":{"rendered":"LOI.GAMMA.N"},"content":{"rendered":"

Description et Syntaxe<\/h2>\n

La fonction LOI.GAMMA.N dans Microsoft Excel et GAMMA.DIST dans Google Sheets est utilis\u00e9e pour calculer la probabilit\u00e9 que la variable al\u00e9atoire d’une distribution gamma soit inf\u00e9rieure ou \u00e9gale \u00e0 une valeur x donn\u00e9e. C’est une fonction tr\u00e8s utile dans les analyses statistiques, en particulier pour les distributions asym\u00e9triques qui sont fr\u00e9quemment rencontr\u00e9es dans les \u00e9tudes de fiabilit\u00e9 et d’autres tests de dur\u00e9e de vie.<\/p>\n

La syntaxe pour cette fonction dans les deux logiciels est structur\u00e9e comme suit :<\/p>\n

  GAMMA.DIST(x, alpha, beta, cumulative) LOI.GAMMA.N(x; alpha; beta; cumulative) <\/code> <\/pre>\n
    \n
  • x<\/code> est la valeur de la variable pour laquelle la fonction est calcul\u00e9e.<\/li>\n
  • alpha<\/code> est un param\u00e8tre de la distribution, souvent appel\u00e9 le param\u00e8tre de forme.<\/li>\n
  • beta<\/code> est un autre param\u00e8tre de la distribution, connu comme le param\u00e8tre d’\u00e9chelle.<\/li>\n
  • cumulative<\/code> est un param\u00e8tre logique qui d\u00e9termine la forme de la fonction : TRUE pour la fonction de distribution cumulative, FALSE pour la fonction de densit\u00e9 de probabilit\u00e9.<\/li>\n<\/ul>\n
    Exemples<\/h2>\n
    Exemple 1: Calcul de la densit\u00e9 de probabilit\u00e9<\/p>\n
      =LOI.GAMMA.N(4; 9; 2; FAUX) =GAMMA.DIST(4, 9, 2, FALSE) <\/code> <\/pre>\n
    Dans cet exemple, nous voulons conna\u00eetre la densit\u00e9 de probabilit\u00e9 que la variable al\u00e9atoire d’une distribution gamma avec un param\u00e8tre de forme de 9 et un param\u00e8tre d’\u00e9chelle de 2 prenne la valeur 4. La fonction retournera un nombre repr\u00e9sentant cette densit\u00e9.<\/p>\n
    Exemple 2: Calcul de la distribution cumulative<\/p>\n
      =LOI.GAMMA.N(10; 5; 3; VRAI) =GAMMA.DIST(10, 5, 3, TRUE) <\/code> <\/pre>\n
    Cette fois, nous souhaitons calculer la probabilit\u00e9 cumulative que notre variable al\u00e9atoire soit inf\u00e9rieure ou \u00e9gale \u00e0 10 sous les m\u00eames param\u00e8tres de forme (5) et d’\u00e9chelle (3). Cela nous donne la probabilit\u00e9 cumul\u00e9e jusqu’\u00e0 la valeur 10.<\/p>\n
    Cas pratiques d’utilisation<\/h2>\n
    Premier cas : Analyse de la dur\u00e9e de vie d’un produit<\/p>\n
    Supposons que la durabilit\u00e9 d’un certain composant \u00e9lectronique soit model\u00e9e par une distribution gamma avec un alpha (forme) de 7.5 et un beta (\u00e9chelle) de 3.2. Pour trouver la probabilit\u00e9 que ce composant \u00e9choue avant 8 heures, nous utiliserions :<\/p>\n
      =LOI.GAMMA.N(8; 7.5; 3.2; VRAI) =GAMMA.DIST(8, 7.5, 3.2, TRUE) <\/code> <\/pre>\n
    Cet exemple peut aider les ing\u00e9nieurs en fiabilit\u00e9 \u00e0 d\u00e9finir les intervalles de maintenance ou les garanties pour leurs produits.<\/p>\n
    Deuxi\u00e8me cas : Mod\u00e9lisation du temps n\u00e9cessaire pour compl\u00e9ter une t\u00e2che<\/p>\n
    Imaginons que le temps requis pour compl\u00e9ter un certain type de t\u00e2che informatique est mod\u00e9lis\u00e9 par une distribution gamma avec des param\u00e8tres de forme de 2 et d’\u00e9chelle de 5. Pour d\u00e9terminer la densit\u00e9 de probabilit\u00e9 que la t\u00e2che soit achev\u00e9e exactement \u00e0 10 heures, on calculerait :<\/p>\n
      =LOI.GAMMA.N(10; 2; 5; FAUX) =GAMMA.DIST(10, 2, 5, FALSE) <\/code> <\/pre>\n
    Ce calcul pourrait \u00eatre utile dans la planification des ressources ou l’optimisation des processus dans un environnement de travail. <\/p>\n
    Ces exemples montrent comment la fonction LOI.GAMMA.N dans Excel et GAMMA.DIST dans Google Sheets peuvent \u00eatre appliqu\u00e9es \u00e0 des probl\u00e8mes r\u00e9els, offrant des insights pr\u00e9cieux pour diverses analyses statistiques et d\u00e9cisionnelles.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Renvoie la pRobabilit\u00e9 d\u2019une vaRiable al\u00e9atoiRe suivant une loi Gamma<\/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-6563","post","type-post","status-publish","format-standard","hentry","category-statistiques"],"acf":[],"yoast_head":"\nFonction GAMMA.DIST (LOI.GAMMA.N) dans Excel : comment \u00e7a marche, exemples et syntaxe<\/title>\n<meta name=\"description\" content=\"Pr\u00e9sentation de la fonction GAMMA.DIST (LOI.GAMMA.N) d\u2019Excel et Google Sheets. 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