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

[Departement_IRSTEA]Eaux [TR1_IRSTEA]RIVAGEInternational audienceIn 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