GNU Scientific Library – Reference Manual: The Landau Distribution

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### 20.12 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.