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.

A B S T R A C TThe maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) for the parameters of a multivariate geometric distribution (MGD) have been derived. A modification of the MLE estimator (modified MLE) has been derived in which case the bias is reduced. The mean square error (MSE) of the modified MLE is less than the MSE of the MLE. Variances of the parameters and the corresponding generalized variance (GV) has been obtained. It has been shown that the MLE and modified MLE are consistent estimators. A comparison of the GVs of modified MLE and UMVUE has shown that the modified MLE is more efficient than the UMVUE. In the final section its application has been discussed with an example of actual data.This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).