  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.
