Normalized centered moments of the Fréchet extreme-value distribution and inference of its parameter

03/27/2023

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by   Jean-Christophe Pain, et al.

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In the present work, we provide the general expression of the normalized centered moments of the Fréchet extreme-value distribution. In order to try to represent a set of data corresponding to rare events by a Fréchet distribution, it is important to be able to determine its characteristic parameter α. Such a parameter can be deduced from the variance (proportional to the square of the Full Width at Half Maximum) of the studied distribution. However, the corresponding equation requires a numerical resolution. We propose two simple estimates of α from the knowledge of the variance, based on the Laurent series of the Gamma function. The most accurate expression involves the Apéry constant.