The index of coincidence for the binomial distribution is log-convex
Classical Analysis and ODEs
2017-06-19 v1
Abstract
We consider the binomial distribution with parameters and , and show that the sum of the squared probabilities is a log-convex function of . This completes the proof of a conjecture formulated in 2014. Applications to R\'{e}nyi and Tsallis entropies are given.
Cite
@article{arxiv.1706.05178,
title = {The index of coincidence for the binomial distribution is log-convex},
author = {Ioan Rasa},
journal= {arXiv preprint arXiv:1706.05178},
year = {2017}
}