Bayesian Estimation using Metropolis-Hastings Algorithm of Gumbel Type-II Distribution

Abstract

This research aims to compare the performance of the parameter estimation by the Bayesian approach of the Gumbel type-II distribution on four methods, namely independent metropolis-hastings algorithm, random walk metropolis algorithm, independent metropolis-hastings algorithm with Gibbs sampling, and random walk metropolis algorithm with Gibbs sampling. The comparison among methods is made in terms of the mean square errors based on the Monte Caro simulation technique. The shape parameters were chosen to be 0.5, 1, 2, 3, and 4, the scale parameters were chosen to be 0.5, 1, and 2 and the sample sizes were chosen to be 20, 50, and 100. The prior distribution of both parameters was assumed to be the Gamma distribution. Moreover, we apply four methods for real data. The findings show that the random walk metropolis algorithm and the independent metropolis-hastings algorithm with Gibbs sampling present the best performance in most cases under a simulation study. For real data, the independent metropolis hastings algorithm with Gibbs sampling offers the best performance.