Estimation of P[Y < X] for generalized exponential distribution in presence of outlier

This paper deals with the estimation of P(Y < X), where Y has generalized exponential distribution with parameters a and A and X has mixture gen- eralized exponential distribution (or marginal distribution of X\, X2, Xn, in presence of one outlier with parameters fix and fa) such that X and Y are independent, when the scale parameter (A) is known the maximum like- lihood estimator of R = P(Y < X) is derived. Analysis of a simulated data set has also been presented for illustrative purposes.