# The Beta Distribution¶

gsl_ran_beta(a, 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 $$0 \leq x \leq 1$$.

gsl_ran_beta_pdf(x, a, 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.

gsl_cdf_beta_P(x, a, b)
gsl_cdf_beta_Q(x, a, b)
gsl_cdf_beta_Pinv(P, a, b)
gsl_cdf_beta_Qinv(Q, a, b)

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