Cauchy Distribution

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

Figure 1. Cauchy distribution: (a) probability density, (b) distribution function

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