Estimation of for generalized Pareto distribution

This paper deals with the estimation of P [ Y < X ] when X and Y are two independent generalized Pareto distributions with different parameters. The maximum likelihood estimator and its asymptotic distribution are obtained. An asymptotic confidence interval of P [ Y < X ] is constructed using the asymptotic distribution. Assuming that the common scale parameter is known, MLE, UMVUE, Bayes estimation of R and confidence interval are obtained. The ML estimator of R, asymptotic distribution and Bayes estimation of R in general case is also studied. Monte Carlo simulations are performed to compare the different proposed methods.