Statistical inference of the exponentiated exponential distribution based on progressive type-II censoring with optimal scheme

Abstract

This article is concerned with the estimation of parameters, reliability and hazard rate functions of the exponentiated exponential distribution under progressive type-II censoring data. The maximum likelihood estimation and maximum product of spacing methods are presented to estimate the unknown parameters of the model in classical theme. In the Bayesian paradigm, we have considered both likelihood as well as product of spacing functions to estimates of the model parameters, reliability and hazard rate functions. Bayes estimates are considered under squared error loss function (SELF) using gamma prior for the shape parameter and a discrete prior for the scale parameter. Asymptotic confidence and highest posterior density credible intervals have also been obtained for the model parameters and reliability characteristics. Optimal criteria is also employed to find the best censoring scheme among the considered censoring schemes. A Monte Carlo simulation study is used to compare the performances the derived estimators under different progressive type-II censoring schemes. Finally, to illustrate the practical application of the proposed methodology, two real data analysis are conducted.