— Function: double gsl_ran_beta (const gsl_rng * r, double a, double b)

This function returns a random variate from the beta distribution. The distribution function is,

          p(x) dx = {\Gamma(a+b) \over \Gamma(a) \Gamma(b)} x^{a-1} (1-x)^{b-1} dx

for 0 <= x <= 1.

— Function: double gsl_ran_beta_pdf (double x, double a, double b)

This function computes the probability density p(x) at x for a beta distribution with parameters a and b, using the formula given above.

— Function: double gsl_cdf_beta_P (double x, double a, double b)
— Function: double gsl_cdf_beta_Q (double x, double a, double b)
— Function: double gsl_cdf_beta_Pinv (double P, double a, double b)
— Function: double gsl_cdf_beta_Qinv (double Q, double a, double b)

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