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Extended fractional cumulative past and paired ϕ-entropy measures

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  • Saha, Shital
  • Kayal, Suchandan

Abstract

Very recently, extended fractional cumulative residual entropy (EFCRE) has been proposed by Foroghi et al., (2022). In this paper, we introduce extended fractional cumulative past entropy (EFCPE), which is a dual of the EFCRE. The newly proposed measure depends on the logarithm of fractional order and the cumulative distribution function (CDF). Various properties of the EFCPE have been explored. This measure has been extended to the bivariate setup. Furthermore, the conditional EFCPE is studied and some of its properties are provided. The EFCPE for inactivity time has been proposed. In addition, the extended fractional cumulative paired ϕ-entropy has been introduced and studied. The proposed EFCPE has been estimated using empirical CDF. Furthermore, the EFCPE is studied for coherent systems. A validation of the proposed measure is provided using logistic map. Finally, an application is reported.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:614:y:2023:i:c:s0378437123001073
    DOI: 10.1016/j.physa.2023.128552
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    References listed on IDEAS

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    1. Amarjit Kundu & Asok K. Nanda, 2016. "On study of dynamic survival and cumulative past entropies," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(1), pages 104-122, January.
    2. Wang, Yu & Shang, Pengjian, 2020. "Complexity analysis of time series based on generalized fractional order cumulative residual distribution entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. Jorge Navarro & Yolanda del Águila & Miguel A. Sordo & Alfonso Suárez‐Llorens, 2014. "Preservation of reliability classes under the formation of coherent systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(4), pages 444-454, July.
    4. 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.
    5. 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.
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