Some Results of Generalized Extropy Measure and Its application
Keywords:
Extropy measure; Residual and past extropy measure; Generalized extropy measure; Interval extropy.
Abstract
Taking into account the importance of extropy (see Lad et al. 2015), and its various generalizations, in the present communication we consider and study the generalized extropy of order alpha and type beta based on Varma's (Varma, 1966) information measure for both discrete and continuous random variables. The dynamic versions (residual and past, both) of the proposed generalized extropy measure have also been presented. At the end, the interval generalized extropy measure and an application of the proposed generalized extropy measure are also presented.References
Ajith, K. K., and Abdul Sathar, E. I. (2020). Some results on dynamic weighted Varma’s entropy and its applications. American Journal of Mathematical and Management Sciences, 39(1), 90-98.
Buono, F., Kamari, O., and Longobardi, M. (2023). Interval extropy and weighted interval extropy. Ricerche di Matematica, 72(1), 283-298.
Ebrahimi, N. (1996). How to measure uncertainty in the residual life time distribution. SankhyÄ: The Indian Journal of Statistics, Series A, 48-56.
James, R. G., and Crutchfield, J. P. (2017). Multivariate dependence beyond Shannon information. Entropy, 19(10), 531.
Kayal, S. (2016). On generalized cumulative entropies. Probability in the Engineering and Informational Sciences, 30(4), 640-662.
Kundu, C., and Singh, S. (2020). On generalized interval entropy. Communications in Statistics-Theory and Methods, 49(8), 1989-2007.
Krishnan, A. S., Sunoj, S. M., and Unnikrishnan Nair, N. (2020). Some reliability properties of extropy for residual and past lifetime random variables. Journal of the Korean Statistical Society, 49, 457-474.
Kumar, V. (2015). Generalized entropy measure in record values and its applications. Statistics and Probability Letters, 106, 46-51.
Kumar, V., and Singh, N. (2018). Quantile-based generalized entropy of order $\alpha$ and type $\beta $for order statistics. Statistica, 78(4), 299-318.
Kumar, V., and Taneja, H. C. (2011). Some characterization results on generalized cumulative residual entropy measure. Statistics and probability letters, 81(8), 1072-1077.
Lad, F., Sanfilippo, G., and Agro, G. (2015). Extropy: Complementary dual of entropy.Stat Sci 30(1):40-58.
Liu, J., and Xiao, F. (2021). Renyi extropy. Communications in Statistics-Theory and Methods, 52(16), 5836-5847.
Mohamed, M. S., Alsadat, N., and Balogun, O. S. (2023). Continuous Tsallis and Renyi extropy with pharmaceutical market application. AIMS Mathematics, 8(10), 24176-24195.
Rényi, A. (1961, January). 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, pp. 547-562). University of California Press.
Shannon, C. E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27(3), 379-423.
Singh, S. (2021). On some generalized entropy measure for a doubly truncated random variable. Doctoral dissertation, Rajiv Gandhi Institute of Petroleum Technology.
Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of statistical physics, 52, 479-487.
Varma, R. S. (1966). Generalizations of Renyi’s entropy of order $\alpha$. Journal of Mathematical Sciences, 1(7), 34-48.
Zhang, Z. (2023). Entropy-Based Statistics and Their Applications. Entropy, 25(6), 936.
Buono, F., Kamari, O., and Longobardi, M. (2023). Interval extropy and weighted interval extropy. Ricerche di Matematica, 72(1), 283-298.
Ebrahimi, N. (1996). How to measure uncertainty in the residual life time distribution. SankhyÄ: The Indian Journal of Statistics, Series A, 48-56.
James, R. G., and Crutchfield, J. P. (2017). Multivariate dependence beyond Shannon information. Entropy, 19(10), 531.
Kayal, S. (2016). On generalized cumulative entropies. Probability in the Engineering and Informational Sciences, 30(4), 640-662.
Kundu, C., and Singh, S. (2020). On generalized interval entropy. Communications in Statistics-Theory and Methods, 49(8), 1989-2007.
Krishnan, A. S., Sunoj, S. M., and Unnikrishnan Nair, N. (2020). Some reliability properties of extropy for residual and past lifetime random variables. Journal of the Korean Statistical Society, 49, 457-474.
Kumar, V. (2015). Generalized entropy measure in record values and its applications. Statistics and Probability Letters, 106, 46-51.
Kumar, V., and Singh, N. (2018). Quantile-based generalized entropy of order $\alpha$ and type $\beta $for order statistics. Statistica, 78(4), 299-318.
Kumar, V., and Taneja, H. C. (2011). Some characterization results on generalized cumulative residual entropy measure. Statistics and probability letters, 81(8), 1072-1077.
Lad, F., Sanfilippo, G., and Agro, G. (2015). Extropy: Complementary dual of entropy.Stat Sci 30(1):40-58.
Liu, J., and Xiao, F. (2021). Renyi extropy. Communications in Statistics-Theory and Methods, 52(16), 5836-5847.
Mohamed, M. S., Alsadat, N., and Balogun, O. S. (2023). Continuous Tsallis and Renyi extropy with pharmaceutical market application. AIMS Mathematics, 8(10), 24176-24195.
Rényi, A. (1961, January). 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, pp. 547-562). University of California Press.
Shannon, C. E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27(3), 379-423.
Singh, S. (2021). On some generalized entropy measure for a doubly truncated random variable. Doctoral dissertation, Rajiv Gandhi Institute of Petroleum Technology.
Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of statistical physics, 52, 479-487.
Varma, R. S. (1966). Generalizations of Renyi’s entropy of order $\alpha$. Journal of Mathematical Sciences, 1(7), 34-48.
Zhang, Z. (2023). Entropy-Based Statistics and Their Applications. Entropy, 25(6), 936.
Published
2025-01-10
How to Cite
Kumar, V., Sharma, S., & Goel, R. (2025). Some Results of Generalized Extropy Measure and Its application. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2075
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Section
Research Articles
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