Landaupdf

Definition

prob = landaupdf(x,mu,sigma) returns the probability density function at each of the values in \(x\) using the Landau distribution with location paramter \(\mu\) and scale parameter \(\sigma\).

\[p(x|\mu,\sigma)={\frac {1}{\pi \sigma}}\int _{0}^{\infty }e^{-t}\cos \left(t\left({\frac {x-\mu }{\sigma}}\right)+{\frac {2t}{\pi }}\log \left({\frac {t}{\sigma}}\right)\right)\,dt\]

Syntax

double landaupdf(double x, double mu, double sigma)

Parameters

x

Input, double. \(x \geq 0\)

mu

Input, double. Location parameter of the Landau distribution \((-\infty < \mu< \infty)\).

sigma

Input, double. Scale parameter of the Landau distribution \(( 0< \sigma< \infty)\).

Examples

landaupdf(3, 1, 2) = 0.1031123258564