Inferences on Parametric Estimation of Distribution Tails

Abstract

We propose a general method for parameter estimation of a distribution tail that does not depend on the fulfillment of the conditions of the Gnedenko theorem. We prove the consistency of the proposed estimator and its asymptotic normality under stronger conditions imposed on the parametric family of distribution tails. Additionally, the proposed method is adapted for estimating the Weibull and log-Weibull tail indices.