The Epanechnikov–Aradhana Distribution: A Transformation-Based Extension for Reliability and Lifetime Data Analysis

This paper introduces the Epanechnikov–Aradhana Distribution (EAD), a new one-parameter lifetime distribution obtained by applying an Epanechnikov-weighted transformation to the Aradhana baseline distribution. The proposed model preserves the polynomial–exponential structure of the classical Aradhana distribution while modifying its distributional shape through a cumulative distribution function transformation. Closed-form expressions for the probability density function, cumulative distribution function, reliability function, hazard rate function, reversed hazard rate function, and several statistical properties are derived. Parameter estimation is performed using the maximum likelihood method, and the finite-sample performance of the estimator is investigated through Monte Carlo simulation. The practical applicability of the proposed model is illustrated using six real datasets from reliability, material-strength, and survival-analysis applications. The empirical performance of the EAD model is evaluated relative to the baseline Aradhana distribution using likelihood-based and goodness-of-fit measures. The results indicate that the proposed transformation provides a useful extension of the classical Aradhana model and yields improved goodness-of-fit measures for the datasets considered in this study.