# 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 $\gamma >0$.