20.15 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.