A study on comparisons of Bayesian and classical parameter estimation methods for the two-parameter Weibull distribution

Authors : Asuman YILMAZ, Mahmut KARA, Halil AYDOĞDU

Pages : 576-602

Doi:10.31801/cfsuasmas.606890

View : 12 | Download : 6

Publication Date : 2020-06-30

Article Type : Research Paper

Abstract :The main objective of this paper is to determine the best estimators of the shape and scale parameters of the two parameter Weibull distribution. Therefore, both classical and Bayesian approximation methods are considered. For parameter estimation of classical approximation methods maximum likelihood estimators insert ignore into journalissuearticles values(MLEs);, modified maximum likelihood estimators-I insert ignore into journalissuearticles values(MMLEs-I);, modified maximum likelihood estimators -II insert ignore into journalissuearticles values(MMLEs-II);, least square estimators insert ignore into journalissuearticles values(LSEs);, weighted least square estimators insert ignore into journalissuearticles values(WLSEs);, percentile estimators insert ignore into journalissuearticles values(PEs);, moment estimators insert ignore into journalissuearticles values(MEs);, L-moment estimators insert ignore into journalissuearticles values(LMEs); and TL- moment estimators insert ignore into journalissuearticles values(TLMEs); are used. Since the Bayesian estimators don`t have the explicit form. There are Bayes estimators are obtained by using Lindley`s and Tierney Kadane`s approximation methods in this study. In Bayesian approximation, the choice of loss function and prior distribution is very important. Hence, Bayes estimators are given based on both the non- informative and informative prior distribution. Moreover, these estimators have been calculated under different symmetric and asymmetric loss functions. The performance of classical and Bayesian estimators are compared with respect to their biases and MSEs through a simulation study. Finally, a real data set taken from Turkish State Meteorological Service is analysed for better understanding of methods presented in this paper.
Keywords : Bayes approximation, , parameter estimation, , new estimator, L moment estimator, simulation study