3.5.3.2.3 Cauchypdf

Description

The Cauchy distribution, also called the Lorentzian distribution or Lorentz distribution, is a continuous distribution describing resonance behavior.

Definition

Y = cauchypdf(X, x0, \gamma) returns the pdf of the cauchy distribution with location parameter x0 and scale parameter \gamma, evaluated at the values in X.

f(x| x0, \gamma) = \frac{1}{\pi \gamma \left[1 + \left(\frac{x - x0}{\gamma}\right)^2\right]}
 = { 1 \over \pi } \left[ { \gamma \over (x - x0)^2 + \gamma^2  } \right],

Parameters

x (input, double)
dataset
x0 (input, double)
location parameter
\gamma (input, double)
scale parameter \gamma >0.

See Also

exppdf, gampdf, Lappdf, Lognpdf, Normpdf, Poisspdf