Quantile-based Matusita’s overlap measure for past lifetimes

In many practical situations, assessing the similarity between the probability distributions of past lifetimes from two populations is of significant interest. Matusita’s overlap measure in the context of past lifetimes, which quantifies the degree of overlap between two populations based on their probability distributions, provides a widely used metric for such comparisons. In this article, we develop a quantile-based framework for evaluating Matusita’s measure in the context of past lifetimes. The quantile-based approach is particularly advantageous when any of the underlying distributions does not have a closed-form expression for its cumulative distribution function, but its quantile function is explicitly available. We investigate key theoretical properties of the proposed measure, including its bounds and its properties under monotonic transformations. We also propose a nonparametric estimator of the quantile-based Matusita’s measure for past lifetimes and assess its performance through a comprehensive simulation study. In addition, a real data analysis is conducted to illustrate the application of the proposed results.