Estimating the Parameters of Mixture Gamma Distributions Using Maximum Likelihood and Bayesian Method

Abstract

     This paper focuses on the mixture Gamma distribution and uses the maximum likelihood and Bayesian techniques to estimate its parameters. This study uses Expectation Maximization Algorithm (EM) to find the maximum likelihood estimators and the random Metropolis-Hastings algorithm is used to simulate the Bayesian estimates of the parameters of mixture gamma distribution. then these estimates are compared by using the sum of the modulus of the  bias (MBias), and  the  root-mean square error (RMSE). It has  been shown that the Bayesian estimator is better than the maximum likelihood estimator. 

Keywords

• gamma distribution
• mixture distribution
• bayesian estimation
• likelihood function
• expectation maximization algorithm
• metropolis-hastings