Inequalities for indices of coincidence and entropies

Abstract

We consider a probability distribution depending on a real parameter $x$. As functions of $x$, the R\'enyi 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.