Inference on P(X<Y) for bivariate normal distribution based on ranked set sample

In this paper, we consider the problem of estimation of R=P(X<Y), when X and Y are dependent, using bivariate ranked set sampling. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of R are obtained based on ranked set sample when (X,Y) follows bivariate normal distribution. BEs are obtained based on both symmetric and asymmetric loss functions. The percentile bootstrap and HPD confidence intervals for R are also obtained. Simulation studies are carried out to find the accuracy of the proposed estimators. A real data is also used to illustrate the inferential procedures developed in this paper.