Estimation for Parameters of Life of the Marshall‐Olkin Generalized‐Exponential Distribution Using Progressive Type‐II Censored Data

A new three‐parameter extension of the generalized‐exponential distribution, which has various hazard rates that can be increasing, decreasing, bathtub, or inverted tub, known as the Marshall‐Olkin generalized‐exponential (MOGE) distribution has been considered. So, this article addresses the problem of estimating the unknown parameters and survival characteristics of the three‐parameter MOGE lifetime distribution when the sample is obtained from progressive type‐II censoring via maximum likelihood and Bayesian approaches. Making use of the s‐normality of classical estimators, two types of approximate confidence intervals are constructed via the observed Fisher information matrix. Using gamma conjugate priors, the Bayes estimators against the squared‐error and linear‐exponential loss functions are derived. As expected, the Bayes estimates are not explicitly expressed, thus the Markov chain Monte Carlo techniques are implemented to approximate the Bayes point estimates and to construct the associated highest posterior density credible intervals. The performance of proposed estimators is evaluated via some numerical comparisons and some specific recommendations are also made. We further discuss the issue of determining the optimum progressive censoring plan among different competing censoring plans using three optimality criteria. Finally, two real‐life datasets are analyzed to demonstrate how the proposed methods can be used in real‐life scenarios.