# Cauchy Distribution

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## 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.## 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.