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Cumulative and relative cumulative residual information generating measures and associated properties

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  • Omid Kharazmi
  • Narayanaswamy Balakrishnan

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.

Suggested Citation

  • Omid Kharazmi & Narayanaswamy Balakrishnan, 2023. "Cumulative and relative cumulative residual information generating measures and associated properties," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(15), pages 5260-5273, August.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:15:p:5260-5273
    DOI: 10.1080/03610926.2021.2005100
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    Cited by:

    1. Marco Capaldo & Antonio Di Crescenzo & Alessandra Meoli, 2024. "Cumulative information generating function and generalized Gini functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(7), pages 775-803, October.

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