The index of coincidence for the binomial distribution is log-convex

2017/06/16 by Ioan Raşa, Rasa, Ioan
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability and Statistical Research #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1706.05178

openalex publication_date 2017/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the binomial distribution with parameters n and x, and show that the sum of the squared probabilities is a log-convex function of x. This completes the proof of a conjecture formulated in 2014. Applications to Rényi and Tsallis entropies are given.

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