The paper deals with the asymptotic laws of functionals of standard exponential random variables. These classes of statistics are closely related to estimators of the extreme value index when the underlying distribution function is in the Weibull domain of attraction. We use techniques based on martingales theory to describe the non Gaussian asymptotic distribution of the aforementioned statistics. We provide results of a simulation study as well as statistical tests that may be of interest with the proposed results

Abstract. English : We present a new exponential inequality as a

Abstract. Association between random variables is a generalization of independence of these random variables. This concept is more and more commonly used in current trends in any research fields in Statistics. In this paper, we proceed to a simple, clear and rigorous introduction to it. We will present the fundamental asymptotic normality theorem on stationary and associated sequences of random variables. A coherent and modern frame is used. This review will be profitable to new resarchers in the topic.Résumé. Le concept de variables aléatoires associées est une généralisation de l'indépendance entre variables aléatoires. Il devient de plus en plus important dans les probabilités et les applications statistiques de tous les jours. Dans ce papier, nous introduisonsà ce concept et présentons le théorème fondamental de la normalité asymptotique de sommes partielles d'une suite stationnaire de variables aléatoires associées. Nous utilisons un cadre moderne et cohérent qui sera profitable aux chercheurs débutants dans ce domaine.

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