## 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).

## 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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