Comparison Of Maximum Likelihood And Bayes Estimators Under Symmetric And Asymmetric Loss Functions By Means Of Tierney Kadane’s Approximation For Weibull Distribution

Year 2019, Volume: 14 Issue: 2, 69 - 78, 27.09.2019

Gülcan Gencer , Kerem Gencer

Abstract

In this study, it is considered the problem
of comparing the performances of the Maximum Likelihood (ML) and Bayes
estimators under symmetric and asymmetric loss function  for the unknown parameters of Weibull
distribution. ML estimators are computed by using the Newton Raphson method. Bayesian
estimations under Squared, Linex and General Entropy loss functions by using
Jeffrey’s extension prior are introduced with Tierney Kadane approximation for
Weibull distribution. For different sample sizes, estimators are compared to
obtain the best estimator in terms of mean squared errors using a Monte Carlo
simulation study.

Keywords

Tierney-Kadane’s approximation, Bayes estimator, Weibull distribution, Maximum likelihood estimation, Loss Functions

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