A Comparison of Parameter Estimation Using Maximum Likelihood Estimation and Method of Moment for Shanker Distribution

Abstract

The research aims to study and compare the efficiency of estimating the parameters of the Shanker distribution between the maximum likelihood estimation (MLE) and the method of moment (MOM) methods by simulating the data when setting = 0.3, 0.5, 1.0, 1.5 and 2.5, respectively. The sample sizes used in the study were 20, 40, 60, 80 and 100. In addition, both parameter estimation methods are applied for real data with goodness-of-fit tests presented. The results of the simulation study showed that the maximum likelihood method (MLE) and the method of moments (MOM) were effective in estimating the parameters of the Shanker distribution because they gave an estimate that approached the true value as the sample size increased. Considering the absolute value of BIAS, it is found that the MLE method gives a lower absolute value of BIAS than the MOM method, except for = 0.3 and 0.5 (< 1) and n = 80 and 100, where the MOM method gives a lower absolute value of BIAS than the MLE method. However, the MOM method has a lower variance than the MLE method. From the comparison of the parameter estimation of both methods with the three real datasets, it is found that the MLE method gives estimates that are more consistent with the real datasets than the MOM method. On the other hand, the MOM method gives a faster number of rounds to converge to the answer than the MLE method.