Cumulative and relative cumulative residual information generating measures and associated properties

Omid Kharazmi and Narayanaswamy Balakrishnan

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 15, 5260-5273

Abstract: In this work, we propose cumulative residual information generating (CRIG) and relative cumulative residual information generating (RCRIG) measures and then establish some of their properties. A new divergence measure based on the CRIG function is proposed to measure the closeness between two survival functions as well as a cumulative residual Kullback-Leibler divergence. We also present Jensen-cumulative residual information generating function, whose derivatives generate some new cumulative information measures such as Jensen-cumulative residual Taneja entropy, Jensen-fractional cumulative residual entropy and Jensen-Gini mean difference measure. We further show that the Jensen-cumulative residual information generating function can be expressed as a mixture of two versions of the proposed new divergence measure.

Date: 2023
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DOI: 10.1080/03610926.2021.2005100

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