# Cauchypdf

## Description

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

## Definition

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

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

## Parameters

x (input, double)
dataset
a (input, double)
location parameter
b (input, double)
scale parameter $b >0$.