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Bivariate extension of generalized cumulative past entropy

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  • Amarjit Kundu
  • Chanchal Kundu

Abstract

The cumulative past entropy (CPE) of order α, a dual measure of cumulative residual entropy (CRE) of order α, has recently been proposed as a suitable extension of CPE. In this article, we extend the definition of (dynamic) CPE of order α (DCPE(α)) to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending DCPE(α) for conditionally specified models. Several properties, including monotonicity, and bounds of DCPE(α) are obtained for conditional distributions. Along with some characterization results it is shown that the proposed generalized measure uniquely determines the distribution function. Moreover, we also propose a stochastic order based on this measure and prove interrelation with some existing stochastic orders.

Suggested Citation

  • Amarjit Kundu & Chanchal Kundu, 2018. "Bivariate extension of generalized cumulative past entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(8), pages 1962-1977, April.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:8:p:1962-1977
    DOI: 10.1080/03610926.2017.1335412
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    Cited by:

    1. 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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