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Bivariate extension of (dynamic) cumulative past entropy

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  • Amarjit Kundu
  • Chanchal Kundu

Abstract

Recently, the concept of cumulative residual entropy (CRE) has been studied by many researchers in higher dimensions. In this article, we extend the definition of (dynamic) cumulative past entropy (DCPE), a dual measure of (dynamic) CRE, to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending DCPE for conditionally specified models. Several properties, including monotonicity, and bounds of DCPE are obtained for conditional distributions. It is shown that the proposed measure uniquely determines the distribution function. Moreover, we also propose a stochastic order based on this measure.

Suggested Citation

  • Amarjit Kundu & Chanchal Kundu, 2017. "Bivariate extension of (dynamic) cumulative past entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(9), pages 4163-4180, May.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:9:p:4163-4180
    DOI: 10.1080/03610926.2015.1080838
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    Cited by:

    1. Nair Rohini S. & Abdul Sathar E. I., 2019. "Bivariate Dynamic Weighted Survival Entropy of Order 𝛼," Stochastics and Quality Control, De Gruyter, vol. 34(2), pages 67-85, December.
    2. Amit Ghosh & Chanchal Kundu, 2019. "Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures," Statistical Papers, Springer, vol. 60(6), pages 2225-2252, December.
    3. Saha, Shital & Kayal, Suchandan, 2023. "Extended fractional cumulative past and paired ϕ-entropy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).

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