Cumulative and relative cumulative residual information generating measures and associated properties

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.

Keywords:

• Information generating function
• Jensen-information generating function
• Jensen-Shannon entropy
• survival function
• Jensen-Gini mean difference
• Kullback-Leibler divergence

Acknowledgments

The authors thank the reviewer for useful comments which led to an improvement in this manuscript.