Extremes

, Volume 19, Issue 1, pp 25–40 | Cite as

A limiting distribution for maxima of discrete stationary triangular arrays with an application to risk due to avalanches

  • Pascal Sielenou Dkengne
  • Nicolas Eckert
  • Philippe Naveau
Article

Abstract

In this paper, we generalize earlier work dealing with maxima of discrete random variables. We show that row-wise stationary block maxima of a triangular array of integer valued random variables converge to a Gumbel extreme value distribution if row-wise variances grow sufficiently fast as the row-size increases. As a by-product, we derive analytical expressions of normalising constants for most classical unbounded discrete distributions. A brief simulation illustrates our theoretical result. Also, we highlight its usefulness in practice with a real risk assessment problem, namely the evaluation of extreme avalanche occurrence numbers in the French Alps.

Keywords

Extreme values Triangular arrays Stationary processes Discrete random variables Snow avalanche occurrence numbers 

AMS 2000 Subject Classifications

60G70 60G10 60F10 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Pascal Sielenou Dkengne
    • 1
  • Nicolas Eckert
    • 1
  • Philippe Naveau
    • 2
  1. 1.IRSTEA, UR ETGR Erosion torrentielle neige et avalanchesUniversité de Grenoble Alpes, IRSTEA, 2 rue de la PapeterieGrenobleFrance
  2. 2.Laboratoire des Sciences du Climat et l’Environnement (LSCE) CNRSGif-sur-YvetteFrance

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