Confidence interval estimation of P(Y<X) in the Gamma Case

This paper is concerned with the problem of interval estimation of R = P(Y<X) when X and Y are independent gamma random variables. We compare ten different confidence interval estimators. An important thrust of this paper is to employ bootstrapping methodology to address the problem of robustness with respect to the shape parameters of the gamma distributions. We believe that bootstrapping provides a powerful methodology for studying these problems. Seven of the ten confidence interval estimators considered are based on bootstrapping. Simulation results are presented and discussed, with robustness recommendations.