Exploring Lomax-Gumbel {Frechet} Distribution in the Bayesian Paradigm

Abstract

This paper explores the Lomax-Gumbel {Frechet} distribution in the Bayesian paradigm. The posterior distributions of the parameters are not attained in closed form, so the Lindley and the Tierney-Kadane approximation methods are used for the evaluation of Bayes estimators and associated posterior risks under uniform, Maxwell, and half logistic priors. A complete implementation of these two techniques is provided. Three loss functions are used. An extensive simulation study and two real life data are provided to obtain and compare Bayes estimators in terms of prior distributions and loss functions. It is reported that the Bayes estimators obtained through the Tierney-Kadane method give better results than the Lindley approximation method, in terms of minimum posterior risks.