  We present a new family of estimators of the Weibull tail-coefficient. The
Weibull tail-coefficient is defined as the regular variation coefficient of the
inverse failure rate function. Our estimators are based on a linear combination
of log-spacings of the upper order statistics. Their asymptotic normality is
established and illustrated for two particular cases of estimators in this
family. Their finite sample performances are presented on a simulation study.
