BOUNDS FOR INDICES OF COINCIDENCE AND ENTROPIES

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Acu A., BAŞCANBAZ TUNCA G., Rasa I.

MATHEMATICAL INEQUALITIES & APPLICATIONS, cilt.24, sa.2, ss.307-321, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.7153/mia-2021-24-22
  • Dergi Adı: MATHEMATICAL INEQUALITIES & APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.307-321
  • Anahtar Kelimeler: Probability distribution, index of coincidence, bounds for entropies, convex functions, stochastic majorization technique
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper we consider a parameterized family of discrete probability distributions and investigate the Renyi,Tsallis, and Shannon entropies associated with them. Lower and upper bounds for these entropies are obtained, improving some results from the literature. The proofs are based on several methods from classical analysis, theory of dual cones, and the stochastic majorization theory. The Renyi and Tsallis entropies are naturally expressed in terms of the index of coincidence. Consequently we study in detail the index of coincidence associated to the corresponding discrete probability distributions. The obtained results lead immediately to properties of the entropies.