Estimating P(Y < X) when X and Y are paired exponential variables

Inference procedures for gamma = P (T-2 < T-1) are considered when T-1 and T-2 are correlated and distributed as bivariate exponential. Under this model, asymptotic inference procedures based on maximum likelihood. the method of moments, and generalized estimating equations are developed. Exact confidence limits and the bootstrap BCa confidence on gamma are also given. Monte Carlo methods are used to estimate the coverage probabilities with the aim of evaluating the alternative strategies. Two examples are given to illustrate these techniques.