Estimation of the Weibull tail-coefficient with linear combination of upper order statistics

TL;DR

This paper introduces a new family of estimators for the Weibull tail-coefficient using linear combinations of upper order statistics, with proven asymptotic properties and demonstrated finite sample performance.

Contribution

It proposes a novel class of estimators for the Weibull tail-coefficient based on log-spacings, with theoretical asymptotic normality and empirical validation.

Findings

Establishes asymptotic normality of the estimators.

Demonstrates good finite sample performance through simulations.

Provides two specific estimator cases within the proposed family.

Abstract

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.