Exploring weighted Tsallis extropy: Insights and applications to human health

Ramy Abdelhamid Aldallal; Haroon M. Barakat; Mohamed Said Mohamed; Ramy Abdelhamid Aldallal; Haroon M. Barakat; Mohamed Said Mohamed

doi:10.3934/math.2025102

AIMS Mathematics

2025, Volume 10, Issue 2: 2191-2222. doi: 10.3934/math.2025102

Previous Article Next Article

Research article Special Issues

Exploring weighted Tsallis extropy: Insights and applications to human health

1.
Department of Management, College of Business Administration in Hawtat Bani Tamim, Prince Sattam bin Abdulaziz University, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
3.
Mathematics Department, Faculty of Education, Ain Shams University, Cairo 11341, Egypt

Received: 20 November 2024 Revised: 15 January 2025 Accepted: 17 January 2025 Published: 08 February 2025
MSC : 62B99, 62H30, 94A15, 94A17

This article presents the notion of the continuous case of the weighted Tsallis extropy function as an information measure that follows the framework of continuous distribution. We introduce this concept from two perspectives, depending on the extropy and weighted Tsallis entropy. Various examples to illustrate the two perspectives of the weighted Tsallis extropy by examining a few of its characteristics are presented. Some features and stochastic orders of those measures, including the maximum value, are introduced. An alternative depiction of the proposed models concerning the hazard rate function is provided. Furthermore, the order statistics of the weighted Tsallis extropy and their lower bounds are considered. Moreover, the bivariate Tsallis extropy and its weighted version are derived. Non-parametric estimators are also derived for the new measures under cancer-related fatalities in the European Union countries data. Additionally, a pattern recognition comparison between Tsallis extropy and weighted Tsallis extropy is presented.
- extropy,
- weighted Tsallis entropy,
- hazard rate function,
- stochastic orders,
- order statistics,
- non-parametric estimation
Citation: Ramy Abdelhamid Aldallal, Haroon M. Barakat, Mohamed Said Mohamed. Exploring weighted Tsallis extropy: Insights and applications to human health[J]. AIMS Mathematics, 2025, 10(2): 2191-2222. doi: 10.3934/math.2025102

Related Papers:

Abstract

This article presents the notion of the continuous case of the weighted Tsallis extropy function as an information measure that follows the framework of continuous distribution. We introduce this concept from two perspectives, depending on the extropy and weighted Tsallis entropy. Various examples to illustrate the two perspectives of the weighted Tsallis extropy by examining a few of its characteristics are presented. Some features and stochastic orders of those measures, including the maximum value, are introduced. An alternative depiction of the proposed models concerning the hazard rate function is provided. Furthermore, the order statistics of the weighted Tsallis extropy and their lower bounds are considered. Moreover, the bivariate Tsallis extropy and its weighted version are derived. Non-parametric estimators are also derived for the new measures under cancer-related fatalities in the European Union countries data. Additionally, a pattern recognition comparison between Tsallis extropy and weighted Tsallis extropy is presented.

References

[1]	C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J., 27 (1948), 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x doi: 10.1002/j.1538-7305.1948.tb01338.x
[2]	S. Guiasu, Weighted entropy, Rep. Math. Phys., 2 (1971), 165–179. https://doi.org/10.1016/0034-4877(71)90002-4 doi: 10.1016/0034-4877(71)90002-4
[3]	C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 52 (1988), 479–487. https://doi.org/10.1007/BF01016429 doi: 10.1007/BF01016429
[4]	M. S. Mohamed, H. M. Barakat, S. A. Alyami, M. A. A. Elgawad, Cumulative residual Tsallis entropy-based test of uniformity and some new findings, Mathematics, 10 (2022), 771. https://doi.org/10.3390/math10050771 doi: 10.3390/math10050771
[5]	S. Behera, J. E. Contreras-Reyes, S. Kayal, Mutual information matrix and global measure based on Tsallis entropy, Nonlinear Dyn., 2024. https://doi.org/10.1007/s11071-024-10469-2 doi: 10.1007/s11071-024-10469-2
[6]	O. Nicolis, J. Mateu, J. E. Contreras-Reyes, Wavelet-based entropy measures to characterize two-dimensional fractional Brownian fields, Entropy, 22 (2020), 196. https://doi.org/10.3390/e22020196 doi: 10.3390/e22020196
[7]	R. Maya, M. R. Irshad, C. Chesneau, F. Buono, M. Longobardi, Non-parametric estimation of Tsallis entropy and residual Tsallis entropy under $\rho$-mixing dependent data, In: Flexible nonparametric curve estimation, Cham: Springer, 2024, 95–112. https://doi.org/10.1007/978-3-031-66501-1_5
[8]	N. Balakrishnan, F. Buono, M. Longobardi, A unified formulation of entropy and its application, Phys. A, 596 (2022), 127214. https://doi.org/10.1016/j.physa.2022.127214 doi: 10.1016/j.physa.2022.127214
[9]	S. Das, On weighted generalized entropy, Commun. Stat. Theory Methods, 46 (2017), 5707–5727. https://doi.org/10.1080/03610926.2014.960583 doi: 10.1080/03610926.2014.960583
[10]	F. Lad, G. Sanfilippo, G. Agro, Extropy: Complementary dual of entropy, Statist. Sci., 30 (2015), 40–58. https://doi.org/10.1214/14-STS430 doi: 10.1214/14-STS430
[11]	M. Z. Raqab, G. Qiu, On extropy properties of ranked set sampling, Statistics, 53 (2019), 210–226. https://doi.org/10.1080/02331888.2018.1533963 doi: 10.1080/02331888.2018.1533963
[12]	G. Qiu, The extropy of order statistics and record values, Stat. Probab. Lett., 120 (2017), 52–60. https://doi.org/10.1016/j.spl.2016.09.016 doi: 10.1016/j.spl.2016.09.016
[13]	N. Balakrishnan, F. Buono, M. Longobardi, On Tsallis extropy with an application to pattern recognition, Stat. Probab. Lett., 180 (2022), 109241. https://doi.org/10.1016/j.spl.2021.109241 doi: 10.1016/j.spl.2021.109241
[14]	F. Buono, Y. Deng, M. Longobardi, The unified extropy and its versions in classical and Dempster-Shafer theories, J. Appl. Probab., 61 (2024), 685–696. https://doi.org/10.1017/jpr.2023.68 doi: 10.1017/jpr.2023.68
[15]	M. S. Mohamed, N. Alsadat, O. S. Balogun, Continuous Tsallis and Renyi extropy with pharmaceutical market application, AIMS Mathematics, 8 (2023), 24176–24195. https://doi.org/10.3934/math.20231233 doi: 10.3934/math.20231233
[16]	M. S. Mohamed, H. M. Barakat, A. A. Mutairi, M. S. Mustafa, Further properties of Tsallis extropy and some of its related measures, AIMS Mathematics, 8 (2023), 28219–28245. https://doi.org/10.3934/math.20231445 doi: 10.3934/math.20231445
[17]	E. I. A. Sathar, R. D. Nair, On dynamic weighted extropy, J. Comput. Appl. Math., 393 (2021), 113507. https://doi.org/10.1016/j.cam.2021.113507 doi: 10.1016/j.cam.2021.113507
[18]	N. Balakrishnan, F. Buono, M. Longobardi, On weighted extropies, Comm. Statist. Theory Methods, 51 (2022), 6250–6267. https://doi.org/10.1080/03610926.2020.1860222 doi: 10.1080/03610926.2020.1860222
[19]	N. Gupta, S. K. Chaudhary, On general weighted extropy of ranked set sampling, Commun. Stat. Theory Methods, 53 (2023), 4428–4441. https://doi.org/10.1080/03610926.2023.2179888 doi: 10.1080/03610926.2023.2179888
[20]	S. K. Chaudhary, N. Gupta, P. K. Sahu, On general weighted cumulative residual extropy and general weighted negative cumulative extropy, Statistics, 57 (2023), 1117–1141. https://doi.org/10.1080/02331888.2023.2241595 doi: 10.1080/02331888.2023.2241595
[21]	M. R. Irshad, K. Archana, R. Maya, M. Longobardi, Estimation of weighted extropy with focus on its use in reliability modeling, Entropy, 26 (2024), 160. https://doi.org/10.3390/e26020160 doi: 10.3390/e26020160
[22]	S. Bansal, N. Gupta, Weighted extropies and past extropy of order statistics and k-record values, Comm. Statist. Theory Methods, 51 (2022), 6091–6108. https://doi.org/10.1080/03610926.2020.1853773 doi: 10.1080/03610926.2020.1853773
[23]	M. Shaked, J. G. Shanthikumar, Stochastic orders, New York: Springer, 2007. https://doi.org/10.1007/978-0-387-34675-5
[24]	J. Jeon, S. Kochar, C. G. Park, Dispersive ordering—Some applications and examples, Statist. Papers, 47 (2006), 227–247. https://doi.org/10.1007/s00362-005-0285-4 doi: 10.1007/s00362-005-0285-4
[25]	N. Ebrahimi, N. Maasoumi, E. S. Soofi, Ordering univariate distributions by entropy and variance, J. Econometrics, 90 (1999), 317–336. https://doi.org/10.1016/S0304-4076(98)00046-3 doi: 10.1016/S0304-4076(98)00046-3
[26]	O. Kharazmi, J. E. Contreras-Reyes, N. Balakrishnan, Optimal information, Jensen-RIG function, and $\alpha$-Onicescu's correlation coefficient in terms of information generating functions, Phys. A, 609 (2023), 128362. https://doi.org/10.1016/j.physa.2023.128362 doi: 10.1016/j.physa.2023.128362
[27]	H. A. David, H. N. Nagaraja, Order statistics, John Wiley & Sons, Inc., 2003.
[28]	H. Wang, W. Chen, B. Li, Large sample properties of maximum likelihood estimator using moving extremes ranked set sampling, J. Korean Stat. Soc., 53 (2024), 398–415. https://doi.org/10.1007/s42952-023-00251-2 doi: 10.1007/s42952-023-00251-2
[29]	S. Chakraborty, O. Das, B. Pradhan, Weighted negative cumulative extropy with application in testing uniformity, Phys. A, 624 (2023), 128957. https://doi.org/10.1016/j.physa.2023.128957 doi: 10.1016/j.physa.2023.128957
[30]	M. Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist., 27 (1956), 832–837. https://doi.org/10.1214/aoms/1177728190 doi: 10.1214/aoms/1177728190
[31]	E. Parzen, On estimation of a probability density function and mode, Ann. Math. Statist., 33 (1962), 1065–1076. https://doi.org/10.1214/aoms/1177704472 doi: 10.1214/aoms/1177704472
[32]	OECD, Deaths from cancer (indicator), 2024. Available from: https://doi.org/10.1787/8ea65c4b-en
[33]	UCI Machine learning repository, 2017. Available from: http://archive.ics.uci.edu/ml
[34]	B. Y. Kang, Y. Li, Y. Deng, Y. J. Zhang, X. Y. Deng, Determination of basic probability assignment based on interval numbers and its application, Acta Electron. Sinica, 40 (2012), 1092–1096. https://doi.org/10.3969/j.issn.0372-2112.2012.06.004 doi: 10.3969/j.issn.0372-2112.2012.06.004

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)