Bayesian Estimation of the Scale Parameter of the Weimal Distribution
Tajan Mashingil Mabur
Department of Statistics, Ahmadu Bello University, Zaria, Kaduna State, Nigeria.
Aisha Omale
Department of Statistics, Ahmadu Bello University, Zaria, Kaduna State, Nigeria.
Ahmed Lawal
Department of Mathematic and Statistics, Hassan Usman Katsina Polytechnic, Katsina, Nigeria.
Mustapha Mohammed Dewu
Centre for Geodesy and Geodynamics, P.M.B 011 Toro, Bauchi State, Nigeria.
Sa’ad Mohammed *
Department of Mathematic and Statistics, Federal Polytechnic, Bauchi, Bauchi State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This article aims at estimating the scale parameter of the Weimal distribution using Bayesian method and comparing the estimators obtained to the estimator of the scale parameter obtained from the method of maximum likelihood. Under Bayesian approach, the estimators are obtained by using uniform prior and Jeffrey’s prior with the adoption of the precautionary, quadratic and square error loss functions. A derivation and discussion2ws under maximum likelihood estimation is also done. The above methods of estimation employed in this paper are compared based on their mean square errors (MSEs) through a simulation study carried out in R statistical software with different sample sizes. The results indicate that the most appropriate method for the scale parameter is precautionary loss function under either uniform or Jeffrey’s prior irrespective of the sample sizes allocated and the values taken by the other parameters.
Keywords: Weimal distribution, Bayesian methods, prior distributions, loss functions, maximum likelihood estimation, mean square error, sample size.