A Comparison of Parameter Estimation of Gamma Distribution by Maximum Likelihood, Bayes’ and Markov Chain Monte Carlo Methods

Abstract

The objective of this research is to estimate a parameter () of gamma distribution by using Maximum Likelihood (ML), Bayes', Markov Chain Monte Carlo (MCMC), and applied Bayes' with Markov Chain Monte Carlo (Bayes'-MCMC) methods. The Bayes' method is depended on the prior distribution, so gamma distribution is consideredthe parameter for Bayes' estimator. The t-test is used for testing that the true parameter is equal the mean of estimated parameter, while it means the performant method for estimating parameter. Data is simulated from gamma distribution by setting the shape parameter () as 4,5,6,7 and 8 and the scale parameter or called true parameter () as 2 based on the sample sizes (n) 30, 50 and 70. The results are found that ML, Bayes', MCMC is a good performance to estimate parametor in most all case except moderate sample size and small shape parameter. The Bayes'-MCMC method outperforms all others when shape parameter and sample sizes are large