The Landau Distribution


This function returns a random variate from the Landau distribution. The probability distribution for Landau random variates is defined analytically by the complex integral,

\[p(x) = (1/(2 \pi i)) \int_{c-i\infty}^{c+i\infty} \exp(s \log(s) + x s) ds\]

For numerical purposes it is more convenient to use the following equivalent form of the integral,

\[p(x) = (1/\pi) \int_0^\infty \exp(-t \log(t) - x t) \sin(\pi t) dt.\]

This function computes the probability density \(p(x)\) at \(x\) for the Landau distribution using an approximation to the formula given above.