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19.11 The Landau Distribution

Function: double gsl_ran_landau (const gsl_rng * r)

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} ds exp(s log(s) + x s) 

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

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

Function: double gsl_ran_landau_pdf (double x)

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