Entropiya o‘lchovlarining nazariy asoslari: Shannon, Reyni va Tsallis entropiyasi taqqoslamasi
DOI:
https://doi.org/10.5281/zenodo.18055485Ключевые слова:
entropiya o‘lchovlari; Shannon entropiyasi; Rényi entropiyasi; Tsallis entropiyasi; axborot nazariyasi; statistik tahlil.Аннотация
Ushbu maqolaning maqsadi Shannon, Rényi va Tsallis entropiya o‘lchovlarining nazariy asoslarini tahlil
qilish hamda ularning matematik va axborot-nazariy xususiyatlarini qiyosiy jihatdan o‘rganishdan iborat. Tadqiqotda entropiya
o‘lchovlarining qo‘llanish doiralari, statistik sezgirligi, hisoblash murakkabligi hamda ularning axborot tizimlarida tahlil
vositasi sifatidagi samaradorligi yoritilgan. O‘tkazilgan qiyosiy tahlillar asosida turli entropiya modellari turli tipdagi ehtimollik
taqsimotlari va murakkab tizimlar uchun qanchalik mos ekanligi aniqlanadi.
Библиографические ссылки
1. Drake, G. W. F. (2025-October-15). Entropy and heat death. Encyclopaedia Britannica.
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3. Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423
4. Rényi, A. (1961). On measures of information and entropy. In Proceedings of the Fourth Berkeley Symposium on
Mathematics, Statistics and Probability (pp. 547–561). University of California Press.
5. Tsallis, C. (1988). Possible generalization of Boltzmann–Gibbs statistics. Journal of Statistical Physics, 52(1–2), 479–
487.
6. Cover, T. M., & Thomas, J. A. (2006). Elements of Information Theory (2nd ed.). Wiley-Interscience.
7. Jaynes, E. T. (1957). Information theory and statistical mechanics. Physical Review, 106(4), 620–630.
8. Khinchin, A. I. (1957). Mathematical Foundations of Information Theory. Dover Publications.
9. Abe, S., & Okamoto, Y. (Eds.). (2001). Nonextensive Statistical Mechanics and Its Applications. Springer.
10. MacKay, D. J. C. (2003). Information Theory, Inference, and Learning Algorithms. Cambridge University Press
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