Chernoff's distribution
In probability theory, Chernoff's distribution, named after Herman Chernoff, is the probability distribution of the random variable
where W is a "two-sided" Wiener process satisfying W = 0.
If
then V has density
where gc has Fourier transform given by
and where Ai is the Airy function. Thus fc is symmetric about 0 and the density ƒZ = ƒ1. Groeneboom shows that
where is the largest zero of the Airy function Ai and where.
