On estimation of cumulative residual extropy and its quantile version

Recently, cumulative residual extropy has been introduced in the literature as an alternative measure of information. We propose two estimators of cumulative residual extropy and compare their performance with existing kernel based estimator by simulation. Asymptotic properties of the estimators are studied. Also we propose two estimators of quantile cumulative residual extropy measure and show that these estimators are consistent and asymptotically normally distributed. Two data sets are analysed for illustrative purposes. The proposed estimators perform reasonably well.

Automated summary

This study proposes two estimators of cumulative residual extropy and compares their performance with an existing kernel based estimator through simulation. The asymptotic properties of the estimators are examined, and two estimators of quantile cumulative residual extropy measure are also proposed, demonstrating their consistency and asymptotic normality. The proposed estimators show good performance through analysis of two data sets.