The binomial distribution maximises entropy among sums of negatively related indicators with fixed mean and support

Source abstract

We show that the binomial distribution supported on $\{0,1,\ldots,n\}$ and with mean $np$ for some $0<p<1$ maximises entropy within the class of sums of negatively related indicator random variables with this mean and support. Our results generalise the main result of Yu (2008), who showed that this binomial distribution maximises entropy within the smaller class of ultra-log-concave random variables of order $n$. Our proof makes use of a Markov chain construction of Yu (2008), together with a stochastic ordering argument.