Cauchy Distribution

(redirected from Lorentz 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.

References in periodicals archive ?
The Lorentz distribution can be expanded into the linear superposition of Hermite-Gaussian functions [36]:
The reason is that the spreading of the Lorentz distribution in the turbulent atmosphere is higher than that of the Gaussian distribution.
Based on the extended Huygens-Fresnel integral and the expansion of Lorentz distribution into Hermite-Gaussian functions, the analytical expressions of the average intensity, the effective beam size, and the kurtosis parameter of a Lorentz-Gauss vortex beam are derived in the turbulent atmosphere, respectively.