Two-parameter Maxwell distribution: Properties and different methods of estimation

ABSTRACT

In this article we consider the problem of estimating location and scale parameters of the Maxwell distribution from both frequentist and Bayesian points of view. Additionally, some properties of the distribution, namely, stochastic ordering, Rényi and Shannon entropies, and order statistics, are derived. Behavior of the estimators from different frequentist approaches, namely, maximum likelihood, method of moments, least square’s, and weighted least square as well as Bayes estimators of parameters, is compared with respect to bias, mean squared errors, and the coverage percentage extracted from bootstrap confidence intervals. The existence and uniqueness of the maximum likelihood estimators are also discussed. The Bayes estimators and the associated credible intervals are obtained using importance sampling technique under squared error loss function. A gamma prior is used for the scale parameter and a uniform prior for the location parameter. An example with flood-level data is used to illustrate applicability of procedures discussed.

KEYWORDS:

• Entropy
• maximum likelihood estimators
• method of moment estimators
• least squares estimators
• Bayes estimators

AMS SUBJECT CLASSIFICATION:

• 60E05
• 62F10
• 62F15

Acknowledgments

The authors thank the reviewers and the editors for their comments, which helped improve the article.