Estimation and prediction for a Burr type-III distribution with progressive censoring

ABSTRACT

We consider estimation of unknown parameters and reliability characteristics of a Burr type-III distribution under progressive censoring. Predictive estimates for censored observations and the associated prediction intervals are also obtained. We derive maximum-likelihood estimators of unknown quantities using the EM algorithm and then also obtain the observed Fisher information matrix. We provide various Bayes estimators for unknown parameters under the squared error loss function. Highest posterior density and asymptotic intervals are also constructed. We evaluate performance of proposed methods using simulations. Finally, an illustrative example is presented in support of the methods discussed.

KEYWORDS:

• Asymptotic confidence interval
• HPD interval
• maximum-likelihood estimator
• MH algorithm
• predictive estimates
• Tierney and Kadane method

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N01
• 62N02

Acknowledgments

The authors are indebted to an anonymous referee for his encouraging suggestions that have led to substantial improvement in the presentation and the content of this manuscript. They also extend their sincere thanks to the Editor and an Associate Editor for their valuable suggestions. Y.M. Tripathi gratefully acknowledges the partial financial support provided by Department of Science and Technology, India [grant number SR/S4/MS : 785/12].