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Jensen-information generating function and its connections to some well-known information measures

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  • Kharazmi, Omid
  • Balakrishnan, Narayanaswamy

Abstract

In this work, we consider the information generating function measure and develop some new results associated with it. We specifically propose two new divergence measures and show that some of the well-known information divergences such as Jensen–Shannon, Jensen-extropy and Jensen–Taneja divergence measures are all special cases of it. Finally, we also discuss the information generating function for residual lifetime variables.

Suggested Citation

  • Kharazmi, Omid & Balakrishnan, Narayanaswamy, 2021. "Jensen-information generating function and its connections to some well-known information measures," Statistics & Probability Letters, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:stapro:v:170:y:2021:i:c:s0167715220302984
    DOI: 10.1016/j.spl.2020.108995
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    References listed on IDEAS

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    1. Bercher, J.-F., 2013. "Some properties of generalized Fisher information in the context of nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3140-3154.
    2. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S. & Zohrevand, Younes, 2016. "Jensen–Shannon information of the coherent system lifetime," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 244-255.
    3. Bercher, J.-F., 2012. "A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4460-4469.
    4. B. Sharma & I. Taneja, 1975. "Entropy of type (α, β) and other generalized measures in information theory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 22(1), pages 205-215, December.
    5. Yaser Mehrali & Majid Asadi & Omid Kharazmi, 2018. "A Jensen–Gini measure of divergence with application in parameter estimation," METRON, Springer;Sapienza Università di Roma, vol. 76(1), pages 115-131, April.
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    Cited by:

    1. Suchandan Kayal & N. Balakrishnan, 2023. "Weighted fractional generalized cumulative past entropy and its properties," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-23, June.
    2. Kharazmi, Omid & Contreras-Reyes, Javier E. & Balakrishnan, Narayanaswamy, 2023. "Optimal information, Jensen-RIG function and α-Onicescu’s correlation coefficient in terms of information generating functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).

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