Estimation in power Lindley distributions using balanced joint progressively Type-II censored data

Abstract

The balanced joint progressive Type-II (BJPT-II) censoring plan has gained enormous popularity in reliability theory and lifetime experiments over the last decade. It is highly applicable when the purpose of an experiment is to compare the relative properties of units drawn from various independent production lines (or populations) under the same environmental conditions. The present article considers the problem of estimation in two power Lindley distributions (PLD) with BJPT-II censored samples. The maximum likelihood estimates of the unknown parameters are computed along with the associated asymptotic confidence intervals. Further, the Bayes estimates are derived with the informative priors for the model parameters under the linear exponential (LINEX) loss function. The construction of the highest posterior density intervals for the unknown model parameters is also carried out under the Bayesian setup. For the Bayesian computations, the Markov chain Monte Carlo (MCMC) techniques are implemented. To exemplify the mathematically developed estimation methods, a computational illustration and a real data analysis are carried out. In order to find an optimum censoring plan, some optimality criteria are also discussed.