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

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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.

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Authors and Affiliations

  1. Department of Statistics, St. Anthony’s College, Shillong, Meghalaya, India

    Sanku Dey

  2. Department of Quantitative Health Sciences, Cleveland Clinic, Cleveland, Ohio, USA

    Tanujit Dey

  3. Department of Decision Sciences, Bocconi University, Milan, Italy

    Sajid Ali

  4. Department of Mathematics and Statistics, University of South Alabama, 411 University Blvd North, ILB 325, 36688-0002, Mobile, Alabama, USA

    Madhuri S. Mulekar

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  1. Sanku Dey
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  2. Tanujit Dey
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  3. Sajid Ali
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  4. Madhuri S. Mulekar
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Correspondence to Madhuri S. Mulekar.

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Dey, S., Dey, T., Ali, S. et al. Two-parameter Maxwell distribution: Properties and different methods of estimation. J Stat Theory Pract 10, 291–310 (2016). https://doi.org/10.1080/15598608.2015.1135090

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  • DOI: https://doi.org/10.1080/15598608.2015.1135090

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