On confidence intervals for P (X < Y )

Abstract

We assume X and Y be two independent random variables and define θ=P (X < Y ). The inference for θ can be found in various fields. This paper not only compares several methods for constructing the confidence interval for θ in a small sample but also proposes some new methods. The intervals derived by these new methods show good performance in a small sample, and their actual coverage probability is close to the nominal level. In addition, one of the biggest advantages of our methods is that it does not require complicated calculations.