The Binomial Parameter Estimation by Using Weighted Method of Maximum Likelihood Estimator and Bayes Estimator

Abstract

The objective of this research is to propose the binomial parameter estimation by using weightedmethod of Maximum Likelihood estimator and Bayes estimator. The used weighted value does theminimum variance estimator. In addition to, this research compares three binomial parameter estimationmethods. Those methods are Maximum Likelihood method, Bayes method, and Weighted method. Theresearch was considered by the mean square errors (MSE). The comparisons were done by using threelevels of sample sizes (n) small (10, 20, and 30), medium (50 and 70) and large (100, 200, and 500) whereasthe population proportions are 0.01, 0.03, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, and 0.50. Thisresearch used the Monte Carlo simulation method. The experiment was repeated 10,000 times for eachcondition. Results of the research are as follows: For all sample sizes, the MSE of Maximum Likelihoodmethod is the lowest when the parameter (p) is not greater than 0.10. For all sample sizes, the MSE ofBayesian method is the lowest when the parameter (p) lies between 0.20 and 0.50. For the sample sizes atleast 30, The MSE of Weighted method is the lowest when the parameter (p) is equal to 0.15.

Keywords : Parameter Estimation / Binomial Distribution / Maximum Likelihood Method /Bayes Method / Weighted Method