An Entropy-Based Scale-Free L-Statistic for Exponentiality Testing in Lifetime Data with DMRL Aging

This paper introduces an entropy-based scale-free L-statistic for exponentiality testing in lifetime data under decreasing mean residual life (DMRL) aging. The proposed method is derived from a mean-residual-life characterization of the DMRL class through a cumulative residual entropy-type departure functional that quantifies deviations from the constant mean residual life property of the exponential distribution. An L-functional representation of this departure measure is established, leading to an order-statistic-based nonparametric test statistic. To remove the effect of the unknown exponential scale parameter, the statistic is normalized by the sample mean, yielding a scale-invariant testing procedure under the null hypothesis. The exact finite-sample null distribution is obtained using normalized spacings, and asymptotic normality is established through standard L-statistic theory. Monte Carlo simulations under linear failure rate, gamma, and Weibull DMRL alternatives show that the proposed test maintains the nominal significance level and provides competitive power relative to existing DMRL procedures. Real-data applications further illustrate the usefulness of the method as an entropy-based statistical tool for detecting DMRL aging patterns in reliability and lifetime-data analysis.