Abstract
We consider a probability distribution depending on a real parameter x. As functions of x, the Renyi entropy and the Tsallis entropy can be expressed in terms of the associated index of coincidence S(x).
We establish recurrence relations and inequalities for S(x), which can be used in order to get information concerning the two entropies.
Authors
Alexandra Măduța
Technical University of Cluj-Napoca, Romania
Diana Otrocol
Technical University of Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
Ioan Rașa
Technical University of Cluj-Napoca, Romania
Keywords
probability distribution; Renyi entropy; Tsallis entropy; index of coincidence; functional equations; inequalities
References
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[3] I. Rasa, Entropies and Heun functions associated with positive linear operators, Appl. Math. Comput., 268(2015), 422–431.
[4] I. Rasa, Convexity properties of some entropies, Results Math., 73:105 (2018).
[5] I. Rasa, Convexity properties of some entropies (II), Results Math., 74:154 (2019).
About this paper
Cite this paper as:
A. Măduța, D. Otrocol, I. Rașa, Inequalities for indices of coincidence and entropies, Arxiv:1910.13491
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