NEW LIMITING DISTRIBUTIONS OF MAXIMA OF INDEPENDENT RANDOM VARIABLES

Abstract: This paper deals with the limiting distribution of the maximum, under linear normalization, of kn independent real random variables, where fkng is a non decreasing positive integer sequence satisfying lim n!+1 kn = +1. It is proven that, if the sequence of random variables veri¯es a new Uniformity Assumption of Maxima depending on the behaviour of the sequence fkng, which is a suitable extension of the Galambos assumption (Galambos, 1978), a new class of limiting distribution of maxima arises in the theory of extremes. This class contains the Mejzler's class of log-concave distributions (Mejzler, 1956) and also the class of max-semistable distributions introduced in Grinevich (1992).