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 Kuş (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.

重叠系数是两种分布之间相似性的直接量度，最近在许多应用领域中变得非常有用，包括微阵列分析，以鉴定差异表达的生物标志物，尤其是在数据遵循多峰分布的情况下。但是，有关重叠系数的推论非常有限，尤其是在包括审查数据在内的不同采样方案下。在本文中，我们考虑了由Wu和Kuş（2009）引入的一种称为“渐进式首次故障检查”的寿命测试方案。基于这种类型的审查，我们推断出三个众所周知的重叠度量，即对两个均值指数种群使用不同均值的Matusita度量，Morisita度量和Weitzman度量。推导了重叠测度估计量的渐近偏差和方差。在小样本情况下，由于难以计算重叠测度的最终估计量的精度或偏差，因此使用了蒙特卡洛评估。这些度量的置信区间也可以通过自举法和泰勒近似法构造。一个真实的数据示例用于说明我们提出的估算器。