GENERALIZED EXTROPY OF k-RECORDS: PROPERTIES AND APPLICATIONS

Abstract

In this paper, we introduce a generalized measure of extropy based on k-records and study its properties. We show that several exist- ing extropies, such as survival, negative cumulative, past and weighted extropy are special cases of this generalized measure of extropy. We also propose a dynamic generalized measure of extropy based on k-records which includes residual extropy, dynamic survival extropy and weighted dynamic survival extropy. A generating function is discussed using this generalized extropy measure, using which we provide different extropy and entropy measures. Some important properties of generalized extropy of k-records and generating function are derived. We use simulation to assess the bias and mean squared error of the estimator of the generalized extropy and compute its values for real data.