Chernoff's density is log-concave

Details Chernoff's density is log-concave Chernoff's density is log-concave

2012-03-05

arxiv.org/abs/1203.0828v1

Mathematics

Statistics Theory

20 pages

Scientific paper

We show that the density of $Z = \argmax \{W(t) - t^2 \}$, 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. We also show that the standard normal density can be written in the same structural form as Chernoff's density, make connections with L. Bondesson's class of hyperbolically completely monotone densities, and identify a large sub-class thereof having log-transforms to $\RR$ which are strongly log-concave.

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