Chernoff’s density is log-concave.

Summary We show that the density of Z = argmaxfW (t) t 2 g, sometimes known as Cherno's density, is log-concave. We conjecture that Cherno's density is strongly log-concave or \super-Gaussian", and provide evidence in support of the conjecture. We also show that the standard normal den- sity can be written in the same structural form as Cherno's density, make connections with L. Bondesson's class of hyperbolically completely mono- tone densities, and identify a large sub-class thereof having log-transforms to R which are strongly log-concave.