Some properties on dynamic cumulative Tsallis residual entropy measures based on Sarmanov family with applications to motor data

M. A. Alawady; H. M. Barakat; Asamh Saleh M. Al Luhayb; G. M. Mansour; M. A. Alawady; H. M. Barakat; Asamh Saleh M. Al Luhayb; G. M. Mansour

doi:10.3934/math.2026340

AIMS Mathematics

2026, Volume 11, Issue 3: 8271-8307. doi: 10.3934/math.2026340

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Some properties on dynamic cumulative Tsallis residual entropy measures based on Sarmanov family with applications to motor data

1.
Department of Statistics and Operations Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
3.
Department of Mathematics, College of Science, Qassim University, P. O. Box 6644, Buraydah 51452, Saudi Arabia

Received: 17 January 2026 Revised: 05 March 2026 Accepted: 11 March 2026 Published: 27 March 2026
MSC : 60B12, 62G30

This study presents Tsallis and Rényi entropies as continuous measures of information for continuous distributions based on concomitants of generalized order statistics from the Sarmanov (SAR) family. Additionally, the characteristics and their relationship to other information measures are presented. One of such measures is the cumulative Tsallis residual entropy (CTRE), which can be regarded as an alternative measure of dispersion, and we study its dynamic version. Moreover, applications of these results are given for order statistics, and the record values as special cases with uniform, Weibull, and exponential marginal distributions. Furthermore, the empirical alternative CTRE (denoted ACTRE) was proposed to estimate these information measures. Finally, a real-world dataset has been examined for illustrative purposes and demonstrates superior goodness-of-fit and interpretability compared with classical bivariate distributions.
- concomitants,
- SAR family,
- entropy,
- Tsallis entropy,
- Rényi entropy,
- cumulative Tsallis residual entropy,
- nonparametric estimation,
- generalized order statistics
Citation: M. A. Alawady, H. M. Barakat, Asamh Saleh M. Al Luhayb, G. M. Mansour. Some properties on dynamic cumulative Tsallis residual entropy measures based on Sarmanov family with applications to motor data[J]. AIMS Mathematics, 2026, 11(3): 8271-8307. doi: 10.3934/math.2026340

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Abstract

This study presents Tsallis and Rényi entropies as continuous measures of information for continuous distributions based on concomitants of generalized order statistics from the Sarmanov (SAR) family. Additionally, the characteristics and their relationship to other information measures are presented. One of such measures is the cumulative Tsallis residual entropy (CTRE), which can be regarded as an alternative measure of dispersion, and we study its dynamic version. Moreover, applications of these results are given for order statistics, and the record values as special cases with uniform, Weibull, and exponential marginal distributions. Furthermore, the empirical alternative CTRE (denoted ACTRE) was proposed to estimate these information measures. Finally, a real-world dataset has been examined for illustrative purposes and demonstrates superior goodness-of-fit and interpretability compared with classical bivariate distributions.

References

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