Sometimes due to complicated form of estimators, we can not compute their variances. In some cases the best way to approximate the variance is using lower bounds such as Cramer-Rao and its extension Bhattacharyya lower bounds. On the other hand, statistical inference for stress-strength measure needs the variance of unbiased estimators. In this paper, we present the maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) of stress- strength reliability measure of form )<(= XYPR , when X and Y have Burr XII distribution. Also, in this distribution, we obtain the general form of Bhattacharyya matrix and then by using Bhattacharyya lower bounds, we approximate the variance of any unbiased estimator of R .

Keywords