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2016•American Journal of Theoretical and Applied StatisticsOpen access

Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions

Lanping Li

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Abstract

The aim of this article is to study the Bayes estimation and minimax estimation of the parameter of Maxwell distribution. Bayes estimators are obtained with non-informative quasi-prior distribution under different loss functions, namely, weighted squared error loss, squared log error loss and entropy loss functions. Then the minimax estimators of the parameter are obtained by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks.

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What this paper is about

The aim of this article is to study the Bayes estimation and minimax estimation of the parameter of Maxwell distribution. Bayes estimators are obtained with non-informative quasi-prior distribution under different loss functions, namely, weighted squared error loss, squared log error loss and entropy loss functions. Then the minimax estimators of the parameter are obtained by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks.

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Available abstract

The aim of this article is to study the Bayes estimation and minimax estimation of the parameter of Maxwell distribution. Bayes estimators are obtained with non-informative quasi-prior distribution under different loss functions, namely, weighted squared error loss, squared log error loss and entropy loss functions. Then the minimax estimators of the parameter are obtained by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks.

Key concepts: Minimax, Estimator, Mathematics, Minimax estimator, Mean squared error, Bayes' theorem, Bayes estimator, Applied mathematics

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