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.
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Dkengne, P.S., Eckert, N. & Naveau, P. A limiting distribution for maxima of discrete stationary triangular arrays with an application to risk due to avalanches. Extremes 19, 25–40 (2016). https://doi.org/10.1007/s10687-015-0234-0
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DOI: https://doi.org/10.1007/s10687-015-0234-0
Keywords
- Extreme values
- Triangular arrays
- Stationary processes
- Discrete random variables
- Snow avalanche occurrence numbers
AMS 2000 Subject Classifications
- 60G70
- 60G10
- 60F10