On Relative Cumulative Extropy, Its Residual (Past) Measures and their Applications in Estimation and Testing

This article introduces a new measure of distance between two probability distributions based on the notion of extropy, called the relative cumulative extropy. A test for goodness-of-fit for standard uniform distribution is developed using relative cumulative extropy and compared its power with some existing well known tests. We extend the measure to its dynamic forms, namely the dynamic relative survival and failure extropies, respectively for the residual and past lifetime random variables. Some characterization theorems using the proposed measures for the additive hazards model, additive dynamic survival extropy model, and exponential distributions are derived. Non-parametric kernel estimators are proposed for the estimation of the dynamic measures and their performance is validated through simulation studies. The application and scope of the relative cumulative extropy measure in the image analysis are further investigated. A real data application to examine the usefulness of the relative cumulative residual extropy is also carried out.