Bennett rate function
= Bennett rate function
{c}
{title2=$\phi(u)=(1+u)\log(1+u)-u$}
The <Bennett rate function> has <Taylor expansion> $\phi(u)=u^2/2-u^3/6+O(u^4)$ near zero. It is the optimized exponent in the <Chernoff bound> based on the <moment-generating function> estimate for the <Bennett inequality>.