  The Weibull tail-coefficient (WTC) plays a crucial role in extreme value
statistics when dealing with Weibull-type tails. Several distributions, such as
normal, Gamma, Weibull, and Logistic distributions, exhibit this type of tail
behaviour. The WTC, denoted by $\theta$, is a parameter in a right-tail
function of the form $ \bar F(x) :=1-F(x) =: {\rm e}^{-H(x)}$, where
$H(x)=-\ln(1-F(x))$ represents a regularly varying cumulative hazard function
with an index of regular variation equal to 1/$\theta$,
$\theta\in\mathbb{R}^{+}$. The commonly used WTC-estimators in literature are
often defined as functions of the log-excesses, making them closely related to
estimators of the extreme value index (EVI) for Pareto-type tails. For a
positive EVI, the classical estimator is the Hill estimator. Generalized means
have been successfully employed in estimating the EVI, leading to reduction of
bias and of root mean square error for appropriate threshold values. In this
study, we propose and investigate new classes of WTC-estimators based on power
$p$ of the log-excesses within a second-order framework. The performance of
these new estimators is evaluated through a large-scale Monte-Carlo simulation
study, comparing them with existing WTC-estimators available in the literature.
