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

Abstract

In this article, two frequentist approaches and a Bayesian approach employing progressive Type II censored data are used to estimate parameters of a unit Gompertz distribution. 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. Both Newton-Raphson and stochastic expectation minimization algorithms are used for computing the MLEs, while Bayes estimates are obtained using both the product of spacing function and the likelihood function. Additionally, the highest posterior density (HPD) credible intervals are compared with the approximate confidence intervals (CIs) for the parameters of the model that were derived using both traditional approaches. Moreover, 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 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.