Inference of R = P[X < Y ] for proportional reversed hazard rate model

The proportional reversed hazard rate model (PRHRM) has been extensively used in the literature to model failure time data. This paper deals with the estimation of R = P[X < Y ] when X and Y are two independent the PRHRM with different parameters. The maximum likelihood estimator of R is proposed. Assuming that the common scale parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator, Bayes estimation and confidence interval of R are obtained. Finally, Analysis of a real data set has also been presented for illustrative purposes.