Continuous Tsallis and Renyi extropy with pharmaceutical market application

Mohamed Said Mohamed; Najwan Alsadat; Oluwafemi Samson Balogun; Mohamed Said Mohamed; Najwan Alsadat; Oluwafemi Samson Balogun

doi:10.3934/math.20231233

AIMS Mathematics

2023, Volume 8, Issue 10: 24176-24195. doi: 10.3934/math.20231233

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Research article

Continuous Tsallis and Renyi extropy with pharmaceutical market application

1.
Mathematics Department, Faculty of Education, Ain Shams University, Cairo 11341, Egypt
2.
Department of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi Arabia
3.
School of Computing, University of Eastern Finland

Received: 05 June 2023 Revised: 29 July 2023 Accepted: 06 August 2023 Published: 11 August 2023
MSC : 62B10, 62H30, 94A17

In this paper, the Tsallis and Renyi extropy is presented as a continuous measure of information under the continuous distribution. Furthermore, the features and their connection to other information measures are introduced. Some stochastic comparisons and results on the order statistics and upper records are given. Moreover, some theorems about the maximum Tsallis and Renyi extropy are discussed. On the other hand, numerical results of the non-parametric estimation of Tsallis extropy are calculated for simulated and real data with application to time series model and its forecasting.
- extropy,
- Tsallis entropy,
- Renyi entropy,
- non-parametric estimation,
- time series
Citation: Mohamed Said Mohamed, Najwan Alsadat, Oluwafemi Samson Balogun. Continuous Tsallis and Renyi extropy with pharmaceutical market application[J]. AIMS Mathematics, 2023, 8(10): 24176-24195. doi: 10.3934/math.20231233

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Abstract

In this paper, the Tsallis and Renyi extropy is presented as a continuous measure of information under the continuous distribution. Furthermore, the features and their connection to other information measures are introduced. Some stochastic comparisons and results on the order statistics and upper records are given. Moreover, some theorems about the maximum Tsallis and Renyi extropy are discussed. On the other hand, numerical results of the non-parametric estimation of Tsallis extropy are calculated for simulated and real data with application to time series model and its forecasting.

References

[1]	C. Aliprantis, O. Burkinshaw, Principles of real analysis, North Holland: Elsevier, 1990. http://dx.doi.org/10.1016/C2009-0-22273-2
[2]	N. Balakrishnan, F. Buono, M. Longobardi, On Tsallis extropy with an application to pattern recognition, Stat. Probabil. Lett., 180 (2022), 109241. http://dx.doi.org/10.1016/j.spl.2021.109241 doi: 10.1016/j.spl.2021.109241
[3]	F. Belzunce, R. Lillo, J. Ruiz, M. Shaked, Stochastic comparisons of nonhomogeneous processes, Probab. Eng. Inform. Sci., 15 (2001), 199–224. http://dx.doi.org/10.1017/S0269964801152058 doi: 10.1017/S0269964801152058
[4]	T. Jawa, N. Fatima, N. Sayed-Ahmed, R. Aldallal, M. Mohamed, Residual and past discrete Tsallis and Renyi extropy with an application to softmax function, Entropy, 24 (2022), 1732. http://dx.doi.org/10.3390/e24121732 doi: 10.3390/e24121732
[5]	F. Lad, G. Sanfilippo, G. Agro, Extropy: complementary dual of entropy, Stat. Sci., 30 (2015), 40–58. http://dx.doi.org/10.1214/14-STS430 doi: 10.1214/14-STS430
[6]	J. Liu, F. Xiao, Renyi extropy, Commun. Stat. Theor. M., 52 (2023), 5836–5847. http://dx.doi.org/10.1080/03610926.2021.2020843
[7]	OECD Health Statistics, Pharmaceutical market, OECD, 2023. http://dx.doi.org/10.1787/data-00545-en
[8]	E. Parzen, On estimation of a probability density function and mode, Ann. Math. Statist., 33 (1962), 1065–1076. http://dx.doi.org/10.1214/aoms/1177704472 doi: 10.1214/aoms/1177704472
[9]	G. Qiu, The extropy of order statistics and record values, Stat. Probabil. Lett., 120 (2017), 52–60. http://dx.doi.org/10.1016/j.spl.2016.09.016 doi: 10.1016/j.spl.2016.09.016
[10]	G. Qiu, K. Jia, Extropy estimators with applications in testing uniformity, J. Nonparametr. Stat., 30 (2018), 182–196. http://dx.doi.org/10.1080/10485252.2017.1404063 doi: 10.1080/10485252.2017.1404063
[11]	M. Raqab, G. Qiu, On extropy properties of ranked set sampling, Statistics, 53 (2019), 210–226. http://dx.doi.org/10.1080/02331888.2018.1533963 doi: 10.1080/02331888.2018.1533963
[12]	A. Renyi, On measures of entropy and information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1961,547–561.
[13]	M. Shaked, J. George Shanthikumar, Stochastic orders, New York: Springer, 2007. http://dx.doi.org/10.1007/978-0-387-34675-5
[14]	C. Shannon, A mathematical theory of communication, Bell System Technical Journal, 27 (1948), 379–423. http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x doi: 10.1002/j.1538-7305.1948.tb01338.x
[15]	C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 52 (1988), 479–487. http://dx.doi.org/10.1007/BF01016429 doi: 10.1007/BF01016429
[16]	F. Xiao, Quantum X-entropy in generalized quantum evidence theory, Inform. Sciences, 643 (2023), 119177. http://dx.doi.org/10.1016/j.ins.2023.119177 doi: 10.1016/j.ins.2023.119177
[17]	F. Xiao, On the maximum entropy negation of a complex-valued distribution, IEEE T. Fuzzy Syst., 29 (2021), 3259–3269. http://dx.doi.org/10.1109/TFUZZ.2020.3016723 doi: 10.1109/TFUZZ.2020.3016723
[18]	F. Xiao, EFMCDM: evidential fuzzy multicriteria decision making based on belief entropy, IEEE T. Fuzzy Syst., 28 (2020), 1477–1491. http://dx.doi.org/10.1109/TFUZZ.2019.2936368 doi: 10.1109/TFUZZ.2019.2936368
[19]	Y. Xue, Y. Deng, Tsallis eXtropy, Commun. Stat. Theor. M., 52 (2023), 751–762. http://dx.doi.org/10.1080/03610926.2021.1921804

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