In the present work, we provide the general expression of the normalized centered moments of the Fr\'echet extreme-value distribution. In order to try to represent a set of data corresponding to rare events by a Fr\'echet distribution, it is important to be able to determine its characteristic parameter $\alpha$. 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 $\alpha$ from the knowledge of the variance, based on the Laurent series of the Gamma function. The most accurate expression involves the Ap\'ery constant.

翻译：本文给出了Fr échet极值分布归一化中心矩的一般表达式。为了用Fr échet分布表示一组对应于稀有事件的数据，确定其特征参数$\alpha$至关重要。该参数可从所研究分布的方差（与半高全宽的平方成正比）推导得出，但对应方程需数值求解。我们基于Gamma函数的Laurent级数，提出了两种利用方差估计$\alpha$的简便方法，其中最精确的表达式涉及Apéry常数。