Chernoff's distribution

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In probability theory, Chernoff's distribution, named after Herman Chernoff, is the probability distribution of the random variable

\underset{s \in \mathbf{R}}{\operatorname{argmax}}\ (W(s) - s^2),

where W is a "two-sided" Wiener process (or two-sided "Brownian motion") satisfying W(0) = 0.

[edit] References

  • Piet Groeneboom and Jon A. Wellner, "Computing Chernoff's Distribution", Journal of Computational and Graphical Statistics, pages 388–400, 2001
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