Bounds for some entropies and special functions


Bărar, Adina, Mocanu, Gabriela, Raluca and Raşa, Ioan


Abstract

carpathian_2018_34_1_09_15_abstract

We consider a family of probability distributions depending on a real parameter and including the binomial, Poisson and negative binomial distributions. The corresponding index of coincidence satisfies a Heun differential equation and is a logarithmically convex function. Combining these facts we get bounds for the index of coincidence, and consequently for Rényi and Tsallis entropies of order 2.

Additional Information

Author(s)

Raşa, Ioan, Mocanu, Gabriela Raluca, Bărar, Adina