Quantile-based reliability analysis of weighted extropy

Abstract

In this paper, we develop a quantile-based framework for weighted extropy and residual weighted extropy for uncertainty quantification in reliability and lifetime analysis. The proposed measures are formulated in terms of the quantile density and hazard quantile functions, providing a flexible alternative to conventional density-based formulations. Explicit expressions are derived for several important lifetime distributions, and fundamental properties, including monotonicity, stochastic ordering, characterization results, and extensions to order statistics, are established. In particular, the proposed weighted measures provide additional discriminatory ability and can distinguish distributions having the same classical extropy. Nonparametric estimators based on order-statistic spacings are also developed, and their finite-sample performance is investigated through simulation studies. Applications to real lifetime datasets further illustrate the practical utility of the proposed methodology. The results demonstrate that quantile-based weighted extropy provides a flexible and useful tool for uncertainty quantification, with potential applications in reliability, survival analysis, and risk assessment.