Estimation of extreme quantiles from heavy and light tailed distributions

In Gardes et al. (2011), a new family of distributions is introduced, depending on two parameters ττ and θθ, which encompasses Pareto-type distributions as well as Weibull tail-distributions. Estimators for θθ and extreme quantiles are also proposed, but they both depend on the unknown parameter ττ, making them useless in practical situations. In this paper, we propose an estimator of ττ which is independent of θθ. Plugging our estimator of ττ in the two previous ones allows us to estimate extreme quantiles from Pareto-type and Weibull tail-distributions in an unified way. The asymptotic distributions of our three new estimators are established and their efficiency is illustrated on a small simulation study and on a real data set.