Two-Parameter Rayleigh Distribution: Different Methods of Estimation

SYNOPTIC ABSTRACT

In this study we have considered different methods of estimation of the unknown parameters of a two-parameter Rayleigh distribution from both the frequentists' and the Bayesian view points. First, we briefly describe different frequentists' approaches: maximum likelihood estimators, method of moments estimators, L-moment estimators, percentile-based estimators, and least squares estimators, and we compare them using extensive numerical simulations. We have also considered Bayesian inferences of the unknown parameters. It is observed that the Bayes estimates and the associated credible intervals cannot be obtained in explicit forms, and we have suggested using an importance sampling technique to compute the Bayes estimates and the associated credible intervals. We analyze one dataset for illustrative purposes.

Key Words and Phrases:

• maximum likelihood estimators
• method of moment estimators
• L-moment estimators
• least squares estimators
• weighted least squares estimators
• percentile-based estimators
• Bayes estimators, asymptotic distribution
• simulation consistent estimators

Acknowledgments

The authors would like to thank the editors and the reviewers who helped to substantially improve this article. The authors are thankful to Professor R. G. Surles for providing the strength data.