An Analysis of Record Statistics based on an Exponentiated Gumbel Model

Abstract

This paper develops a maximum profile likelihood estimator of unknown parameters of the exponentiated Gumbel distribution based on upper record values. We propose an approximate maximum profile likelihood estimator for a scale parameter. In addition, we derive Bayes estimators of unknown parameters of the exponentiated Gumbel distribution using Lindley's approximation under symmetric and asymmetric loss functions. We assess the validity of the proposed method by using real data and compare these estimators based on estimated risk through a Monte Carlo simulation.