Weighted Weibull Distribution: Properties and Estimation

Abstract

We take a closer look at the weighted Weibull distribution. First, we study the structural properties of the probability density function, hazard rate, and mean residual lifetime functions of this distribution. We put forward the estimation for the parameters of the weighted Weibull distribution via maximum likelihood estimation technique. We also obtain expected Fisher’s information matrix, as well as discuss the existence and uniqueness of the maximum likelihood estimates. With regard to Bayesian inference of the unknown parameters, we are using importance sampling technique to calculate Bayes estimates and the corresponding highest posterior density intervals. We perform a data analysis for illustrative purposes.

AMS Subject Classification:

• MSC (2000): 62F15
• 62F10
• 62F99

keywords:

• Bayes estimator
• Expected Fisher’s information matrix
• Importance sampling
• Maximum likelihood estimator
• Weighted Weibull distribution

Acknowledgments

The authors thank the reviewers and the editors, who helped to substantially improve the article. The authors also thank Professor Jayanta K. Ghosh and his student Jyotishka Datta, both at Purdue University, for helpful discussion with Theorem 4.2.1.