Chernoff’s density is log-concave
Fadoua Balabdaoui, Jon A. Wellner · Bernoulli · 2014
We show that the density of $Z=\mathop{\operatorname{argmax}}\{W(t)-t^{2}\}$, sometimes known as Chernoff’s density, is log-concave. We conjecture that Chernoff’s density is strongly log-concave or “super-Gaussian”, and provide evidence in support of the conjecture.