Bayesian Analysis of Two Parameter Weibull Distribution Using Different Loss Functions

Abstract

This paper focuses on the Bayesian technique to estimate the parameters of the Weibull distribution. At this location, we use both informative and non-informative priors. We calculate the estimators and their posterior risks using different asymmetric and symmetric loss functions. Bayes estimators do not have a closed form under these loss functions. Therefore, we use an approximation approach established by Lindley to get the Bayes estimates. A comparative analysis is conducted to compare the suggested estimators using Monte Carlo simulation based on the related posterior risk. We also analyze the impact of distinct loss functions when using various priors.

Keywords

• Bayesian Estimation
• Maximum Likelihood Estimation Lindley Approximation
• Monte Carlo Simulation
• Weibull Distribution