The index of coincidence for the binomial distribution is log-convex
classification
🧮 math.CA
keywords
binomialdistributionlog-convexapplicationscoincidencecompletesconjectureconsider
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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 R\'{e}nyi and Tsallis entropies are given.
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