About: 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 where W is a "two-sided" Wiener process (or two-sided "Brownian motion") satisfying W(0) = 0. If then V(0, c) 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 (1989) shows that The Chernoff distribution should not be confused with the Chernoff geometric distribution (called the Chernoff point in information geometry) induced by the Chernoff information.

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  • 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 (or two-sided "Brownian motion") satisfying W(0) = 0. If then V(0, c) 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 (1989) shows that where is the largest zero of the Airy function Ai and where . In the same paper, Groeneboom also gives an analysis of the process . The connection with the statistical problem of estimating a monotone density is discussed in Groeneboom (1985). The Chernoff distribution should not be confused with the Chernoff geometric distribution (called the Chernoff point in information geometry) induced by the Chernoff information. (en)
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  • 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 (or two-sided "Brownian motion") satisfying W(0) = 0. If then V(0, c) 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 (1989) shows that The Chernoff distribution should not be confused with the Chernoff geometric distribution (called the Chernoff point in information geometry) induced by the Chernoff information. (en)
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  • Chernoff's distribution (en)
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