# The Gamma Distribution¶

gsl_ran_gamma(a, 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.

gsl_ran_gamma_knuth(a, b)

This function returns a gamma variate using the algorithms from Knuth (vol 2).

gsl_ran_gamma_pdf(x, a, 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.

gsl_cdf_gamma_P(x, a, b)
gsl_cdf_gamma_Q(x, a, b)
gsl_cdf_gamma_Pinv(P, a, b)
gsl_cdf_gamma_Qinv(Q, a, b)

These functions compute the cumulative distribution functions $$P(x), Q(x)$$ and their inverses for the gamma distribution with parameters a and b.