Estimators for the Finite Mixture of Rayleigh Model Based on Progressively Censored Data

Abstract

In this article, based on progressively Type-II censored samples from a heterogeneous population that can be represented by a finite mixture of two-component Rayleigh lifetime model, the problem of estimating the parameters and some lifetime parameters (reliability and hazard functions) are considered. Both Bayesian and maximum likelihood estimators are of interest. A class of natural conjugate prior densities is considered in the Bayesian setting. The Bayes estimators are obtained using both the symmetric (squared error) loss function, and the asymmetric (LINEX and General Entropy) loss functions. It has been seen that the estimators obtained can be easily evaluated for this type of censoring by using suitable numerical methods. Finally, the performance of the estimates have been compared on the basis of their simulated maximum square error via a Monte Carlo simulation study.

Keywords:

• Heterogeneous populations
• Lindley's approximation
• Mixture of two-component Rayleigh model
• Monte Carlo simulation
• Progressively censored samples
• Symmetric and asymmetric loss functions

Mathematics Subject Classification:

• 62N02
• 62F10

Acknowledgments

The author would like to thank the Editor and a referee for a very careful reading of the manuscript and for helpful comments which substantially improved the earlier version of the manuscript.