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On cumulative past information generating function

Author

Listed:
  • Santosh Kumar Chaudhary
  • Achintya Roy
  • Nitin Gupta

Abstract

This article studies the cumulative past information-generating function (CPIG) and relative cumulative past information-generating function (RCPIG). We study its properties. We establish its relation with generalized cumulative past entropy (GCPE). We define the multivariate version of the CPIG function. We discuss its connection with system reliability for the k-out-of-n system. We define the CPIG stochastic order and its relation with dispersive order. We provide the results for the CPIG measure of convoluted random variables in terms of the measures of its components. We find some inequalities relating to Shannon entropy, CPIG, and GCPE. Some characterization and estimation results regarding CPIG are also discussed. We study CPIG based on SRS and RSS schemes. We define divergence measures between two random variables: Jensen-cumulative past information-generating function (JCPIG), Jensen fractional cumulative past entropy measure, cumulative past Taneja entropy, and Jensen cumulative past Taneja entropy information measure.

Suggested Citation

  • Santosh Kumar Chaudhary & Achintya Roy & Nitin Gupta, 2025. "On cumulative past information generating function," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(18), pages 5784-5805, September.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:18:p:5784-5805
    DOI: 10.1080/03610926.2024.2446397
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