Estimation of the Parameters of a Bivariate Geometric Distribution

Abstract

The uniformly minimum variance unbiased estimators (UMVUE) of the parameters and reliability functions of a bivariate geometric distribution(BGD) have been derived.The exact variances of the maximum likelihood estimator (MLE) and of UMVUE have been derived and the corresponding mean square errors have been compared.It is found that in some cases UMVUE is better and in some cases MLE is better with respect to the mean square errors. In the final section an example of actual data from the game Cricket’s Indian Premium League 2014 (IPL 2014) has been given.

Keywords

• Bivariate Geometric Distribution
• Maximum Likelihood Estimators
• Uniformly Minimum Variance Unbiased Estimators
• Reliability Functions
• cricket.