Cauchy Distribution(redirected from Lorentzian lineshape)
Cauchy distribution[kō·shē dis·trə′byü·shən]
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.