A New Representation of Some Extropy-Related Measures Based on Probability Density Quantile

This paper offers a new representation of several inaccuracy measures of extropy, based on the probability density quantile. These representations provide an alternative approach for estimating and evaluating the inaccuracy inherent in assumed statistical models. Specifically, we present new representations for Kerridge’s inaccuracy extropy, generalized and simple cumulative residual (past) extropy in the [Formula: see text]th-order statistic, upper and lower [Formula: see text]-records, and maximum and minimum ranked set sampling with unequal samples, all based on the probability density quantile. Additionally, we propose a nonparametric estimator for extropy, cumulative residual, and cumulative past extropy, utilizing the kernel density estimator of the probability density quantile function. These new representations and estimators provide novel methodologies for measuring and estimating extropy-related measures.