Title: Comparative studies between the Bayesian estimation and the maximum likelihood estimation of the parameter of the uniform distribution

Authors: Bao Xu; Di Wang; He Qi

Addresses: Institute of Mathematics, Jilin Normal University, Siping, Jilin, 136000, China ' Institute of Mathematics, Jilin Normal University, Siping, Jilin, 136000, China ' Institute of Mathematics, Jilin Normal University, Siping, Jilin, 136000, China

Abstract: The point estimation of the parameter θ of the uniform distribution U(0, θ) is discussed. The general form of the Bayesian estimation of θ is investigated under the weighted square loss function in the framework of Bayesian statistics, and the precise form of the Bayesian estimation of θ is obtained based on the given Pareto conjugate prior distribution. The comparisons between the Bayesian estimation that obtained in the framework of Bayesian statistics and the maximum likelihood estimation that obtained in the framework of classical statistics are studied from theory and simulation respectively. Results show that the Bayesian estimation of θ under the weighted square loss function is smaller than the maximum likelihood estimation of θ in the framework of classical statistic in numerical value, and the Bayesian estimation that obtained is the maximum likelihood estimations of the corresponding functions of θ, respectively.

Keywords: uniform distribution; geometric probability model; probability distribution function; probability density function; Bayesian estimation; conjugate prior distribution; posterior density function; loss function; posterior risk function; maximum likelihood estimation; simulation investigation; MSE; mean square error.

DOI: 10.1504/IJMIC.2020.114187

International Journal of Modelling, Identification and Control, 2020 Vol.35 No.3, pp.211 - 216

Received: 27 Jan 2020
Accepted: 17 May 2020

Published online: 08 Apr 2021 *

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