On estimation of overlapping measures for exponential populations under progressive first failure censoring

Overlapping coefficient is a direct measure of similarity between two distributions which is recently becoming very useful in many fields of applications including microarray analysis for the purpose of identifying differentially expressed biomarkers, especially in case when data follow multimodal distribution. However, inferences on overlapping coefficient are quite limited especially under different sampling schemes including censored data. In this article we consider a life test scheme called a progressive first-failure censoring scheme introduced by Wu and Kus (2009). Based on this type of censoring, we draw inference about the three well-known measures of overlap, namely Matusita's measure, Morisita's measure and Weitzman's measure for two exponential populations with different means. The asymptotic bias and variance of overlap measures estimators are derived. In small sample cases and due to the difficulty of calculating either the precision or the bias of the resulting estimators of overlap measures, Monte Carlo evaluations are used. Confidence intervals for those measures are also constructed via bootstrap method and Taylor approximation. A real data example is used to illustrate our proposed estimators.