# Cauchy Distribution

(redirected from*Cauchy noise*)

## Cauchy distribution

[kō·shē dis·trə′byü·shən] (statistics)

A distribution function having the form

*M*/[π*M*^{2}+ (*x*-*a*)^{2}], where*x*is the variable and*M*and*a*are constants. Also known as Cauchy frequency distribution.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Cauchy Distribution

a special type of probability distribution of random variables. Introduced by Cauchy, it is marked by the density

The characteristic function is

*f*(*t*) = exp (*μit* − λ ǀ *t* ǀ)

The Cauchy distribution is unimodal and symmetric with respect to the point *x* = μ, which is its mode and median. No

moments of positive order of a Cauchy distribution exist. Figure 1 depicts a Cauchy distribution for μ = 1.5 and λ = 1.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.