Estimation of P(Y<X) for Location-Scale Distributions under Joint Progressively Type-II Right Censoring

In this article, estimation of the probability Q=P(Y < X) when X and Y are two independent but not identically location-scale distributed random variables under the joint progressively Type-II censoring is studied. The maximum likelihood estimation and confidence intervals using asymptotic distribution and two parametric bootstrap resampling methods for parameter Q are explored. A simulation study concentrating mainly on the extreme-value distribution illustrates the accuracy of these confidence intervals. Finally, a numerical example is used to illustrate the proposed methods.