# Inequalities for indices of coincidence and entropies

## 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

[1] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York, (1970).
[2] A. Barar, G. Mocanu, I. Rasa, Heun functions related to entropies, RACSAM, 113(2019), 819–830.
[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).

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##### Cite this paper as:

A. Măduța, D. Otrocol, I. Rașa, Inequalities for indices of coincidence and entropies, Arxiv:1910.13491

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