English

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 nn and xx, and show that the sum of the squared probabilities is a log-convex function of xx. This completes the proof of a conjecture formulated in 2014. Applications to R\'{e}nyi and Tsallis entropies are given.

Keywords

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}
}