Posterior analysis of the compound Rayleigh distribution under balanced loss functions for censored data

ABSTRACT

This paper develops Bayesian analysis in the context of progressively Type II censored data from the compound Rayleigh distribution. The maximum likelihood and Bayes estimates along with associated posterior risks are derived for reliability performances under balanced loss functions by assuming continuous priors for parameters of the distribution. A practical example is used to illustrate the estimation methods. A simulation study has been carried out to compare the performance of estimates. The study indicates that Bayesian estimation should be preferred over maximum likelihood estimation. In Bayesian estimation, the balance general entropy loss function can be effectively employed for optimal decision-making.

KEYWORDS:

• Balanced symmetric and asymmetric loss functions
• Bayesian estimation
• Maximum likelihood estimation
• Monte Carlo simulation
• Posterior risk

MATHEMATICS SUBJECT CLASSIFICATION:

• 62C12
• 62N01
• 62F10
• 62F15
• 62N05

Acknowledgments

The authors are thankful to the honorable Editor-in-chief, Associate editor, and anonymous reviewers for valuable comments and constructive suggestions, which significantly improved the article.