Overlap measures are valuable tools for quantifying the degree of similarity between two probability distributions, with a wide range of applications across various fields of statistics. In this paper, we focus on estimating two important overlap measures, Matusita's measure and Weitzman's measure, for distributions belonging to the proportional hazards and proportional reversed hazards families. These families extend a baseline distribution by modifying its hazard or reversed hazard rate, making them particularly suitable for lifetime data modeling. We develop both maximum likelihood and Bayesian estimators for the overlap measures under these models, assuming parametric forms for the baseline distributions. Bayesian estimation is carried out using Lindley's approximation under the assumption of independent gamma priors, and the corresponding highest posterior density credible intervals are derived using the MCMC method. The performance of the proposed estimators is evaluated through Monte Carlo simulations, examining bias, mean squared error, and coverage probabilities. Applications to real-life data further demonstrate the practical utility of the methods.
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