Likelihood and Bayesian inference for k Lindley populations under joint type-II censoring scheme

Abstract

In lifetime experiments, sometimes censoring is inevitable to save experimental cost and to accelerate execution of the test. For conducting a comparative lifetime experiment of the products, which are from different production lines under the same environmental conditions, the joint type-II censoring scheme is practically much significant. The present article deals with inferences, when jointly type-II censored sample is taken from $k$ Lindley populations. The maximum likelihood estimators of the model parameters are derived with their asymptotic confidence intervals and log-transformed asymptotic confidence intervals. The boot-p and boot-t confidence intervals are also calculated. In order to evaluate the impact of prior information, the parameters are estimated in Bayesian framework based on balanced loss function assuming the informative and non-informative priors. Since the expressions for Bayes estimates cannot be obtained in closed form so the importance sampling and the Gibbs sampling techniques are used. Finally, a Monte Carlo simulation study and a real dataset are given to exemplify all the methods of estimation developed here.

Keywords:

• Balanced loss function
• Bayesian estimation
• Joint type-II censoring
• Maximum-likelihood estimation

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N01
• 62N02
• 62N05
• 62F15
• 62F10

Acknowledgments

The authors express their sincere thanks to the Editor and the anonymous learned reviewer for their constructive comments and suggestions on the earlier version of this article.