A Study on Quantile based Cumulative Residual Extropy of Order Statistics

In recent times, there has been a growing interest among researchers in utilizing quantile-based approaches for assessing the uncertainty associated with random variables. Distinct from traditional distribution function methods, quantile-based measurements offer unique perspectives. This paper investigates the extropy of order statistics by introducing a novel approach based on quantiles and explores its properties. Additionally, we present a nonparametric estimator and its application to this new measure using distributions commonly employed in lifetime data analysis.