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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.44 no.2 Bogotá July/Dec. 2021 Epub Aug 26, 2021
https://doi.org/10.15446/rce.v44n2.86562
Original articles of research
Results on the Fractional Cumulative Residual Entropy of Coherent Systems
Resultados en la entropia residual acumulativa fraccional de sistemas coherentes
1 Department of Statistics, Persian Gulf University, Bushehr, Iran
2 Department of Operation Management, Amsterdam Business School University of Amsterdam, Netherlands
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.
Key words: Fractional cumulative residual entropy; Paired entropy; Coherent systems
Recientemente, Xiong et al. (2019) introdujeron una medida alternativa de incertidumbre conocida como entropía residual acumulativa fraccionada (FCRE). En este articulo, primero, estudiamos algunas propiedades generales de FCRE y su versión dynami. También consideramos una versión de entropía pareada acumulativa fraccionaria para una vida aleatoria. Luego, aplicamos la medida FCRE para la vida útil del sistema coherente con componentes distribuidos de manera idéntica.
Palabras clave: Entropía residual acumulativa fraccionada; Entropía pareada; Sistemas coherentes
Acknowledgement
The authors would like to thank the reviewers for their valuable suggestions and comments.
References
Asadi, M. & Zohrevand, Y. (2007), 'On the dynamic cumulative residual entropy', Journal of Statistical Planning and Inference 137(6), 1931-1941. [ Links ]
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. [ Links ]
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. [ Links ]
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. [ Links ]
Di Crescenzo, A. & Longobardi, M. (2009), 'On cumulative entropies', Journal of Statistical Planning and Inference 139(12), 4072-4087. [ Links ]
Klein, I., Mangold, B. & Doll, M. (2016), 'Cumulative paired '-entropy', Entropy 18(7), 248. [ Links ]
Longobardi, M. (2014), 'Cumulative measures of information and stochastic orders', Ricerche di Matematica 63(1), 209-223. [ Links ]
Murthy, D. P., Xie, M. & Jiang, R. (2004), Weibull Models, Vol. 505, John Wiley & Sons. [ Links ]
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. [ Links ]
Navarro, J. & Psarrakos, G. (2017), 'Characterizations based on generalized cumulative residual entropy functions', Communications in Statistics-Theory and Methods 46(3), 1247-1260. [ Links ]
Psarrakos, G. & Navarro, J. (2013), 'Generalized cumulative residual entropy and record values', Metrika 76(5), 623-640. [ Links ]
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. [ Links ]
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. [ Links ]
Rao, M., Chen, Y., Vemuri, B. C. & Wang, F. (2004), 'Cumulative residual entropy: a new measure of information', IEEE transactions on Information Theory 50(6), 1220-1228. [ Links ]
Shaked, M. & Shanthikumar, J. G. (2007), Stochastic Orders, Springer, New York. [ Links ]
Shannon, C. (1948), 'A mathematical theory of communication', Bell System Technical Journal 27, 379-432. [ Links ]
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. [ Links ]
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. [ Links ]
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. [ Links ]
Ubriaco, M. R. (2009), 'Entropies based on fractional calculus', Physics Letters A 373(30), 2516-2519. [ Links ]
Xiong, H., Shang, P. & Zhang, Y. (2019), 'Fractional cumulative residual entropy', Communications in Nonlinear Science and Numerical Simulation 78, 104879. [ Links ]
Received: April 2019; Accepted: December 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
