Classical and Bayesian Inference of Unit Gompertz Distribution Based on Progressively Type II Censored Data

Abstract

In this article, we study estimation methodologies for parameters of an unit Gompertz distribution based on two frequentist methods and Bayesian method using progressively Type II censored data. In frequentist approach, besides conventional maximum likelihood estimation, maximum product of spacing method is proposed for parameter estimation as an alternative approach to common maximum likelihood method. In order to obtain maximum likelihood estimates, we use both Newton-Raphson and stochastic expectation minimization algorithms, while for obtaining Bayes estimates for unknown parameters of the model, we have considered both traditional likelihood function as well as product of spacing function. Moreover, the approximate confidence intervals of the parameters are obtained under two the frequentist approaches and highest posterior density credible intervals of the parameters are obtained under Bayesian approaches using MCMC approach. In addition, percentile bootstrap technique is utilized to compute confidence intervals. Numerical comparisons are presented of the proposed estimators with respect to various criteria quantities using Monte Carlo simulations. Further, using different optimality criteria, an optimal censoring scheme has been suggested. Besides, one-sample and two-sample prediction problems based on observed sample and appropriate predictive intervals under Bayesian framework are discussed. Finally, to demonstrate the proposed methodology in a real-life scenario, maximum flood level data is considered to show the applicability of the proposed methods.