New Limiting Distributions of Maxima of Independent Random Variables

M. Graça Temido

Abstract: This paper deals with the limiting distribution of the maximum, under linear normalization, of $k_n$ independent real random variables, where $\{k_n\}$ is a non decreasing positive integer sequence satisfying $\lim_{n\rightarrow+\infty}k_n=+\infty$.
It is proven that, if the sequence of random variables verifies a new Uniformity Assumption of Maxima depending on the behaviour of the sequence $\{k_n\}$, 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).

Keywords: extremes; stability; semistability.

Classification (MSC2000): 60XX, 62E20.

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