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.

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The Levy skew alpha-Stable Distribution

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The Flat (Uniform) Distribution