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Revista Colombiana de Estadística
versão impressa ISSN 0120-1751
Rev.Colomb.Estad. vol.45 no.2 Bogotá jul./dez. 2022 Epub 01-Fev-2023
https://doi.org/10.15446/rce.v45n2.96844
Artículos originales de investigación
On Cumulative Residual Renyi's Entropy
Sobre la entropía residual acumulada de Renyi
1 Department of Statistics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran
At the entropy measures and their generalization path, in the direction of statistics and information science, recently, Sunoj & Linu (2012) proposed the cumulative residual Renyi's entropy of order a and its dynamic version and studied its main properties. In this paper, we introduce an alternative We also consider its dynamic version and study their main properties in the context of reliability theory and stochastic orders. We give an estimator of the proposed CRRE and investigate its exact and asymptotic distribution. Numerous examples illustrating the theory are also given.
Key words: Aging classes; Cumulative residual entropy, Mean residual lifetime, Stochastic orders, Shannon entropy, Tsallis entropy
En las medidas de entropía y su camino de generalización, en la dirección de las estadísticas y la ciencia de la información, recientemente, Sunoj & Linu (2012) propuso el residual acumulativo la entropía de Renyi de orden a este artículo presentamos una medida alternativa de la entropía residual consideramos su versión dinámica y estudiamos sus principales propiedades en el contexto de la teoría de la confiabilidad y los órdenes estocásticos. Damos un estimador del CRRE propuesto e investigamos su distribución exacta y asintótica. También se dan numerosos ejemplos que ilustran la teoría.
Palabras clave: Clases de envejecimiento; Entropía residual acumulada; Entropía de Shannon, Entropía de Tsallis; Vida útil residual media; Órdenes estocásticas
References
Abraham, B. & Sankaran, P. (2005), 'Renyi's entropy for residual lifetime distribution', Statistical Papers 46(1), 17-30. [ Links ]
Belzunce, F., Pinar, J. F. & Ruiz, J. M. (2005), 'On testing the dilation order and HNBUE alternatives', Annals of the Institute of Statistical Mathematic 57(4), 803-815. [ Links ]
Crescenzo, A. D. & Longobardi, M. (2009), On cumulative entropies and lifetime estimations, in 'International Work-Conference on the Interplay Between Natural and Artificial Computation', Springer, pp. 132-141. [ Links ]
Farris, F. A. (2010), 'The Gini Index and Measures of Equitability', American Mathematical Monthly 57(12), 851-864. [ Links ]
Helmers, R. (1977), A strong law of large numbers for linear combinations of order statistics, Mathematisc Centrum, Amsterdam. [ Links ]
Nanda, A. K. & Chowdhury, S. (2019), 'Shannon's entropy and Its Generalizations towards Statistics, Reliability and Information Science during 1948-2018', arXiv:1901.09779[stat.OT] . [ Links ]
Navarro, J., del Aguila, Y. & Asadi, M. (2010), 'Some new results on the cumulative residual entropy', Journal of Statistical Planning and Inference 140(1), 310-322. [ Links ]
Rajesh, G. & Sunoj, S. M. (2019), 'Some properties of cumulative Tsallis entropy of order α', Statistical papers 60(3), 583-593 [ Links ]
Rao, M., Chen, Y. & Vemuri, B. (2004), 'Cumulative residual entropy: a new measure of information', IEEE Transactions on Information Theory 50(6), 1220-1228. [ Links ]
Rényi, A. (1961), On measures of entropy and information, in 'Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics', Vol. 4, University of California Press, pp. 547-562. [ Links ]
Shaked, M. & Shanthikumar, J. G. (2007), Stochastic Orders, Springer, New York. [ Links ]
Shannon, C. (1948), 'A mathematical theory of communication', The Bell System Technical Journal 27, 379-423. [ Links ]
Shao, J. (2003), Mathematical Statistics, Springer, New York . [ Links ]
Stigler, S. M. (1974), 'Linear functions of order statistics with smooth weight functions', Annals of Statistics 2, 676-693. [ Links ]
Sunoj, S. M. & Linu, M. N. (2012), 'Dynamic cumulative residual Renyi's entropy', Statistics: A Journal of Theoretical and Applied Statistics 46(1), 41-56. [ Links ]
Wellner, J. A. (1977), 'A Gelivenko-Cantelli theorem and strong laws of large numbers for functions of order statistics', Annals of Statistics 5, 473-480. [ Links ]
Zardasht, V. (2015), 'A test for the increasing convex order based on the cumulative residual entropy', Journal of the Korean Statistical Society 44, 491-497. [ Links ]
Received: June 2021; Accepted: February 2022