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.

Keywords

• EM algorithm
• stochastic EM algorithm
• Lindley's approximation
• importance sampling
• MH algorithm
• optimal censoring