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3.5.3.2.3 Cauchypdf
Contents
Description
The Cauchy distribution, also called the Lorentzian distribution or Lorentz distribution, is a continuous distribution describing resonance behavior.
Definition
/math-3f701940249939f04ffec599fc74661b.png?v=0 "Y = cauchypdf(X, x0, \gamma)")
returns the pdf of the cauchy distribution with location parameter /math-e50eb7598b580311bab8f39bb8f4815b.png?v=0 "x0")
and scale parameter /math-ae539dfcc999c28e25a0f3ae65c1de79.png?v=0 "\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],](/labtalk/de/images/Cauchypdf_(function)/math-eec1b662fda22ea7c7ee9959dafd5147.png?v=0 "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
/math-9dd4e461268c8034f5c8564e155c67a6.png?v=0 "x")
(input, double)- dataset
- (input, double)
- location parameter
- (input, double)
- scale parameter
/math-e243b8724ee0860a2b24f48b7c5c2360.png?v=0 "\gamma >0")
.