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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. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

## 19.14 The Gamma Distribution

Function: double gsl_ran_gamma (const gsl_rng * r, double a, double b)
This function returns a random variate from the gamma distribution. The distribution function is,
p(x) dx = {1 \over \Gamma(a) b^a} x^{a-1} e^{-x/b} dx


for x > 0.

The gamma distribution with an integer parameter a is known as the Erlang distribution.

The variates are computed using the Marsaglia-Tsang fast gamma method. This function for this method was previously called gsl_ran_gamma_mt and can still be accessed using this name.

Function: double gsl_ran_gamma_knuth (const gsl_rng * r, double a, double b)
This function returns a gamma variate using the algorithms from Knuth (vol 2).
Function: double gsl_ran_gamma_pdf (double x, double a, double b)
This function computes the probability density p(x) at x for a gamma distribution with parameters a and b, using the formula given above.

Function: double gsl_cdf_gamma_P (double x, double a, double b)
Function: double gsl_cdf_gamma_Q (double x, double a, double b)
Function: double gsl_cdf_gamma_Pinv (double P, double a, double b)
Function: double gsl_cdf_gamma_Qinv (double Q, double a, double b)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the gamma distribution with parameters a and b.
 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition