The E-Bayesian and hierarchical Bayesian estimations for the proportional reversed hazard rate model based on record values

ABSTRACT

In this paper, E-Bayesian and hierarchical Bayesian estimations of the shape parameter, when the underlying distribution belongs to the proportional reversed hazard rate model, are considered. Maximum likelihood, Bayesian and E-Bayesian estimates of the unknown parameter and reliability function are obtained based on record values. The Bayesian estimates are derived based on squared error and linear–exponential loss functions. It is pointed out that some previously obtained order relations of E-Bayesian estimates are inadequate and these results are improved. The relationship between E-Bayesian and hierarchical Bayesian estimations is obtained under the same loss functions. The comparison of the derived estimates is carried out by using Monte Carlo simulations. A real data set is analysed for an illustration of the findings.

KEYWORDS:

• E-Bayesian estimation
• hierarchical Bayesian estimation
• record values
• proportional reversed hazard rate model
• inverse Weibull distribution

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62F10

Acknowledgments

The author wish to thank Dr. Tuğba Yavuz who checked the Theorems 5.2 and 5.3.

Disclosure statement

No potential conflict of interest was reported by the authors.