New results for tails of probability distributions according to their asymptotic decay

Meitner Cadena (1, 2) , Marie Kratz (2, 3)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 ESSEC Business School
3 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

This paper provides new properties for tails of probability distributions belonging to a class defined according to the asymptotic decay of the tails. This class contains the one of regularly varying tails of distributions. The main results concern the relation between this larger class and the maximum domains of attraction of Fréchet and Gumbel.

Mots clés: asymptotic behavior; maximum domains of attraction; Fréchet; Gumbel; Pickands-Balkema-de Haan theorem; regularly varying function

Domaines: Probabilités [math.PR]

Meitner Cadena, Marie Kratz. New results for tails of probability distributions according to their asymptotic decay. 2015. ⟨hal-01181345⟩