Published

2021-07-12

Results on the Fractional Cumulative Residual Entropy of Coherent Systems

Resultados en la entropia residual acumulativa fraccional de sistemas coherentes

DOI:

https://doi.org/10.15446/rce.v44n2.86562

Keywords:

Fractional cumulative residual entropy, Paired entropy, Coherent systems. (en)
Entropia residual acumulativa fraccionada, Entropia pareada, Sistemas coherentes (es)

Downloads

Authors

  • Saeid Tahmasebi Persian Gulf University
  • Reza Mohammadi Department of Operation Management, Amsterdam Business School University of Amsterdam

Recently, Xiong et al. (2019) introduced an alternative measure of uncertainty known as the fractional cumulative residual entropy (FCRE). In this paper, first, we study some general properties of FCRE and its dynamic version. We also consider a version of fractional cumulative paired entropy for a random lifetime. Then we apply the FCRE measure for the coherent system lifetimes with identically distributed components.

Recientemente, Xiong et al. (2019) introdujeron una medida alternativa de incertidumbre conocida como entropia residual acumulativa fraccionada (FCRE). En este articulo, primero, estudiamos algunas propiedades generales de FCRE y su version dynami. También consideramos una version de entropia pareada acumulativa fraccionaria para una vida aleatoria. Luego, aplicamos la medida FCRE para la vida util del sistema coherente con componentes distribuidos de manera idéntica.

References

Asadi, M. & Zohrevand, Y. (2007), 'On the dynamic cumulative residual entropy', Journal of Statistical Planning and Inference 137(6), 1931-1941. DOI: https://doi.org/10.1016/j.jspi.2006.06.035

Burkschat, M. & Navarro, J. (2018), 'Stochastic comparisons of systems based on sequential order statistics via properties of distorted distributions', Probability in the Engineering and Informational Sciences 32(2), 246-274. DOI: https://doi.org/10.1017/S0269964817000018

Calì, C., Longobardi, M. & Navarro, J. (2020), 'Properties for generalized cumulative past measures of information', Probability in the Engineering and Informational Sciences 34(1), 92-111. DOI: https://doi.org/10.1017/S0269964818000360

Da Costa Bueno, V. & Balakrishnan, N. (2020), 'A cumulative residual inaccuracy measure for coherent systems at component level and under nonhomogeneous poisson processes ', Probability in the Engineering and Informational Sciences pp. 1-26. DOI: https://doi.org/10.1017/S0269964820000637

Di Crescenzo, A. & Longobardi, M. (2009), 'On cumulative entropies', Journal of Statistical Planning and Inference 139(12), 4072-4087. DOI: https://doi.org/10.1016/j.jspi.2009.05.038

Klein, I., Mangold, B. & Doll, M. (2016), 'Cumulative paired '-entropy', Entropy 18(7), 248. DOI: https://doi.org/10.3390/e18070248

Longobardi, M. (2014), 'Cumulative measures of information and stochastic orders', Ricerche di Matematica 63(1), 209-223. DOI: https://doi.org/10.1007/s11587-014-0212-x

Murthy, D. P., Xie, M. & Jiang, R. (2004), Weibull Models, Vol. 505, John Wiley & Sons.

Navarro, J., del Águila, Y., Sordo, M. A. & Suárez-Llorens, A. (2013), 'Stochastic ordering properties for systems with dependent identically distributed components', Applied Stochastic Models in Business and Industry 29(3), 264-278. DOI: https://doi.org/10.1002/asmb.1917

Navarro, J. & Psarrakos, G. (2017), 'Characterizations based on generalized cumulative residual entropy functions', Communications in Statistics-Theory and Methods 46(3), 1247-1260. DOI: https://doi.org/10.1080/03610926.2015.1014111

Psarrakos, G. & Navarro, j. (2013), 'Generalized cumulative residual entropy and record values', Metrika 76(5), 623-640. DOI: https://doi.org/10.1007/s00184-012-0408-6

Psarrakos, G. & Toomaj, A. (2017), 'On the generalized cumulative residual entropy with applications in actuarial science', Journal of Computational and Applied Mathematics 309, 186-199. DOI: https://doi.org/10.1016/j.cam.2016.06.037

Rahimi, S., Tahmasebi, S. & Lak, F. (2020), 'Extended cumulative entropy based on k th lower record values for the coherent systems lifetime', Journal of Inequalities and Applications 2020(1), 1-22. DOI: https://doi.org/10.1186/s13660-020-02464-z

Rao, M., Chen, Y., Vemuri, B. C. & Wang, F. (2004), 'Cumulative residual entropy: a new easure of information', IEEE transactions on Information Theory 50(6), 1220-1228. DOI: https://doi.org/10.1109/TIT.2004.828057

Shaked, M. & Shanthikumar, J. G. (2007), Stochastic Orders, Springer, New York. Shannon, C. (1948), 'A mathematical theory of communication', Bell System Technical Journal 27, 379-432. DOI: https://doi.org/10.1002/j.1538-7305.1948.tb01338.x

Tahmasebi, S., Keshavarz, A., Longobardi, M. & Mohammadi, R. (2020), 'A shiftdependent measure of extended cumulative entropy and iIts applications in blind image quality ', Symmetry 12(2), 316. DOI: https://doi.org/10.3390/sym12020316

Toomaj, A., Di Crescenzo, A. & Doostparast, M. (2018), 'Some results on information properties of coherent systems', Applied Stochastic Models in Business and Industry 34(2), 128-143. DOI: https://doi.org/10.1002/asmb.2277

Toomaj, A., Sunoj, S. M. & Navarro, J. (2017), 'Some properties of the cumulative residual entropy of coherent and mixed systems', Journal of Applied Probability 54(2), 379. DOI: https://doi.org/10.1017/jpr.2017.6

Ubriaco, M. R. (2009), 'Entropies based on fractional calculus', Physics Letters A 373(30), 2516-2519. DOI: https://doi.org/10.1016/j.physleta.2009.05.026

Xiong, H., Shang, P. & Zhang, Y. (2019), 'Fractional cumulative residual entropy', Communications in Nonlinear Science and Numerical Simulation 78, 104879. DOI: https://doi.org/10.1016/j.cnsns.2019.104879

How to Cite

APA

Tahmasebi, S. and Mohammadi, R. . (2021). Results on the Fractional Cumulative Residual Entropy of Coherent Systems. Revista Colombiana de Estadística, 44(2), 225–241. https://doi.org/10.15446/rce.v44n2.86562

ACM

[1]
Tahmasebi, S. and Mohammadi, R. 2021. Results on the Fractional Cumulative Residual Entropy of Coherent Systems. Revista Colombiana de Estadística. 44, 2 (Jul. 2021), 225–241. DOI:https://doi.org/10.15446/rce.v44n2.86562.

ACS

(1)
Tahmasebi, S.; Mohammadi, R. . Results on the Fractional Cumulative Residual Entropy of Coherent Systems. Rev. colomb. estad. 2021, 44, 225-241.

ABNT

TAHMASEBI, S.; MOHAMMADI, R. . Results on the Fractional Cumulative Residual Entropy of Coherent Systems. Revista Colombiana de Estadística, [S. l.], v. 44, n. 2, p. 225–241, 2021. DOI: 10.15446/rce.v44n2.86562. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/86562. Acesso em: 28 mar. 2025.

Chicago

Tahmasebi, Saeid, and Reza Mohammadi. 2021. “Results on the Fractional Cumulative Residual Entropy of Coherent Systems”. Revista Colombiana De Estadística 44 (2):225-41. https://doi.org/10.15446/rce.v44n2.86562.

Harvard

Tahmasebi, S. and Mohammadi, R. . (2021) “Results on the Fractional Cumulative Residual Entropy of Coherent Systems”, Revista Colombiana de Estadística, 44(2), pp. 225–241. doi: 10.15446/rce.v44n2.86562.

IEEE

[1]
S. Tahmasebi and R. . Mohammadi, “Results on the Fractional Cumulative Residual Entropy of Coherent Systems”, Rev. colomb. estad., vol. 44, no. 2, pp. 225–241, Jul. 2021.

MLA

Tahmasebi, S., and R. . Mohammadi. “Results on the Fractional Cumulative Residual Entropy of Coherent Systems”. Revista Colombiana de Estadística, vol. 44, no. 2, July 2021, pp. 225-41, doi:10.15446/rce.v44n2.86562.

Turabian

Tahmasebi, Saeid, and Reza Mohammadi. “Results on the Fractional Cumulative Residual Entropy of Coherent Systems”. Revista Colombiana de Estadística 44, no. 2 (July 12, 2021): 225–241. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/86562.

Vancouver

1.
Tahmasebi S, Mohammadi R. Results on the Fractional Cumulative Residual Entropy of Coherent Systems. Rev. colomb. estad. [Internet]. 2021 Jul. 12 [cited 2025 Mar. 28];44(2):225-41. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/86562

Download Citation

CrossRef Cited-by

CrossRef citations2

1. Shital Saha, Suchandan Kayal. (2023). Extended fractional cumulative past and pairedϕ-entropy measures. Physica A: Statistical Mechanics and its Applications, 614, p.128552. https://doi.org/10.1016/j.physa.2023.128552.

2. Mohamed Kayid, Mansour Shrahili. (2022). Some Further Results on the Fractional Cumulative Entropy. Entropy, 24(8), p.1037. https://doi.org/10.3390/e24081037.

Dimensions

PlumX

Plum Print visual indicator of research metrics
  • Citations
  • Scopus - Citation Indexes: 3
  • Usage
  • SciELO - Full Text Views: 18
  • SciELO - Abstract Views: 3
  • Captures
  • Mendeley - Readers: 4
  • Mendeley - Readers: 1
-
see details

Article abstract page views

303

Downloads

License

Copyright (c) 2021 Revista Colombiana de Estadística

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).