Estimation of theWeibull Tail Coefficient Through the Power Mean-of-Order- p

The Weibull tail coefficient (WTC) is the parameter. in a right-tail function of the type (F) over bar := 1 - F, such that H := - ln (F) over bar is a regularly varying function at infinity with an index of regular variation equal to theta is an element of R+. In a context of extreme value theory for maxima, it is possible to prove that we have an extreme value index (EVI)xi = 0, but usually a very slow rate of convergence. Most of the recent WTCestimators are proportional to the class of Hill EVI-estimators, the average of the log-excesses associated with the k upper order statistics, 1 <= k < n. The interesting performance of EVI-estimators based on generalized means leads us to base theWTC-estimation on the power mean-of-order- p (MOp) EVI-estimators. Consistency of the WTC-estimators is discussed and their performance, for finite samples, is illustrated through a small-scale Monte Carlo simulation study.