Estimation, Prediction and Life Testing Plan for the Exponentiated Gumbel Type-II Progressive Censored Data

Abstract

This article accentuates the estimation and prediction of a three-parameter exponentiated Gumbel type-II (EGT-II) distribution when the data are progressively type-II (PT-II) censored. We obtain maximum likelihood (ML) estimates using expectation maximization (EM) and stochastic expectation maximization (StEM) algorithms.

The existence and uniqueness of the ML estimates are discussed. We construct boot- strap confidence intervals. The Bayes estimates are derived with respect to a general entropy loss function. We adopt Lindley's approximation, importance sampling and Metropolis-Hastings (MH) methods. The highest posterior density credible interval is computed based on MH algorithm. Bayesian predictors and associated Bayesian predictive interval estimates are obtained. A real life data set is considered for the purpose of illustration. Finally, we propose different criteria for comparison of different sampling schemes in order to obtain the optimal sampling scheme.