Order Properties Concerning Tsallis Residual Entropy
Abstract
:1. Introduction
2. Background and Notations
3. Fundamental Results
- 1.
- .
- 2.
- for any .
- 1.
- X is smaller than Y in the dispersive order (and write ) if
- 2.
- X is smaller than Y in the convex transform order (and write ) if the function
4. Closure and Reversed Closure Properties
5. Preservation of Tsallis Quantile Entropy Order in the Proportional Hazard Rate Model
- 1.
- If and , then .
- 2.
- If and , then .
- 1.
- If and , then the functionUsing Lemma 1, we can determine that .
- 2.
- If and , then the functionUsing Lemma 1, we can determine that .
6. Preservation of Tsallis Quantile Entropy Order in the Proportional Reversed Hazard Rate Model
- 1.
- If and , then .
- 2.
- If and , then .
- 1.
- If and , then the functionUsing Lemma 1, we can determine that .
- 2.
- If and , then the functionUsing Lemma 1, we can determine that .
7. Preservation of Tsallis Quantile Entropy Order in the Proportional Odds Model
- 1.
- If and , then .
- 2.
- If and , then .
- 1.
- Assume that and . ThenHence, by Lemma 1, we obtain .
- 2.
- Assume that and . ThenHence, by Lemma 1, we obtain .
8. Preservation of Tsallis Quantile Entropy Order in the Record Values Model
- 1.
- If , then .
- 2.
- If and , then .
- 1.
- If , thenWe have, for any ,
- 2.
- If , then
9. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Sfetcu, R.-C.; Preda, V. Order Properties Concerning Tsallis Residual Entropy. Mathematics 2024, 12, 417. https://doi.org/10.3390/math12030417
Sfetcu R-C, Preda V. Order Properties Concerning Tsallis Residual Entropy. Mathematics. 2024; 12(3):417. https://doi.org/10.3390/math12030417
Chicago/Turabian StyleSfetcu, Răzvan-Cornel, and Vasile Preda. 2024. "Order Properties Concerning Tsallis Residual Entropy" Mathematics 12, no. 3: 417. https://doi.org/10.3390/math12030417
APA StyleSfetcu, R.-C., & Preda, V. (2024). Order Properties Concerning Tsallis Residual Entropy. Mathematics, 12(3), 417. https://doi.org/10.3390/math12030417