Extended fractional cumulative past and paired ϕ-entropy measures

Shital Saha and Suchandan Kayal

Physica A: Statistical Mechanics and its Applications, 2023, vol. 614, issue C

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.

Keywords: EFCPE; Inverse Mittag-Leffler function; Conditional EFCPE; Cumulative paired ϕ-entropy; Empirical EFCPE; Coherent system; Logistic map (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:614:y:2023:i:c:s0378437123001073

DOI: 10.1016/j.physa.2023.128552

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