A limiting distribution for maxima of discrete stationary triangular arrays with an application to risk due to avalanches
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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.
KeywordsExtreme values Triangular arrays Stationary processes Discrete random variables Snow avalanche occurrence numbers
AMS 2000 Subject Classifications60G70 60G10 60F10
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