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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
\(Y = cauchypdf(X, x0, \gamma) \) 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 \(\gamma >0\).