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GNU Scientific Library Reference Manual - Third Edition (v1.12)
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
Paperback (6"x9"), 592 pages, 60 figures
ISBN 0954612078
RRP £24.95 ($39.95)

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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.

ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition