Published January 1, 2021
| Version v1
Journal article
Open
BOUNDS FOR INDICES OF COINCIDENCE AND ENTROPIES
- 1. Lucian Blaga Univ Sibiu, Dept Math & Informat, Sir Dr I Ratiu 5-7, RO-550012 Sibiu, Romania
- 2. Ankara Univ, Fac Sci, Dept Math, Str Dogol, TR-06100 Ankara, Turkey
- 3. Tech Univ Cluj Napoca, Fac Automat & Comp Sci, Dept Math, Str Memorandumului 28, Cluj Napoca, Romania
Description
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.
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