This function returns a random variate from the beta distribution. The distribution function is,
for \(0 \leq x \leq 1\).
This function computes the probability density \(p(x)\) at \(x\) for a beta distribution with parameters a and b, using the formula given above.
These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the beta distribution with parameters a and b.