The smallest uniform upper bound on the distance between the mean and the median of the binomial and Poisson distributions
It is shown that for the binomial and Poisson distributions, the distance between the mean and the median is always less than \(\log 2\). It is the best uniform bound since for every \(0 < \varepsilon < \log 2\) there exist binomial and Poisson distributions for which \(| \text{mean} - \text{median} | > \log 2 - \varepsilon\).
scientific article; zbMATH DE number 761924