Bias and variance estimates for the overlap of two exponential populations

The exponential distribution is one of the most commonly used distributions for modeling survival functions. Even when the hypothesis testing procedure indicates differences in two exponential parameters, there may be considerable overlap between two distributions. In many practical situations, researchers compare survival functions for two populations using testing of hypothesis procedures. However, an overlap coefficient describes the amount of similarity between two distributions. Thus, instead of just looking at the equality of parameters one also needs to estimate the amount of overlap between two distributions. This paper presents estimation of overlap measures and bias and variance of their estimates. To study the behavior of bias and variance of estimates, a Monte Carlo study was conducted, the results of which are presented in this paper. A procedure was developed to construct confidence interval estimates for these overlap measures. Some results are demonstrated using survival data on glioblastoma multiformae patients reported by Burdette and Gerhen (1970).