EM algorithm in estimating the 2- and 3-parameter Burr Type III distributions

Abstract

The Burr Type III distribution has been applied in the study of income, wage and wealth. It is suitable to fit lifetime data since it has flexible shape and controllable scale parameters. The popularity of Burr Type III distribution increases because it has included the characteristics of other distributions such as logistic and exponential. Burr Type III distribution has two categories: First a two-parameter distribution which has two shape parameters and second a three-parameter distribution which has a scale and two shape parameters. Expectation-maximization (EM) algorithm method is selected in this paper to estimate the two- and three-parameter Burr Type III distributions. Complete and censored data are simulated based on the derivation of pdf and cdf in parametric form of Burr Type III distributions. Then, the EM estimates are compared with estimates from maximum likelihood estimation (MLE) approach through mean square error. The best approach results in estimates with a higher approximation to the true parameters are determined. The result shows that the EM algorithm estimates perform better than the MLE estimates for two- and three-parameter Burr Type III distributions in the presence of complete and censored data.