Cauchy Distribution

(redirected from Lorentzian lineshape)

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 gain g falls off from its peak value at [[OMEGA].sub.B] by the typical Lorentzian lineshape:
The resonances in the spectra were fitted semiautomatically to a Lorentzian lineshape model function.
Homogeneous broadening mechanisms usually lead to a Lorentzian lineshape for atomic response while the inhomogeneous mechanism is a random quantity with a Gaussian probability distribution and lineshape (Figure 1).