Inverting the symmetrical beta distribution

Source abstract

We propose a fast algorithm for computing the inverse symmetrical beta distribution. Four series (two around x = 0 and two around x = 1/2) are used to approximate the distribution function, and its inverse is found via Newton's method. This algorithm can be used to generate beta random variates by inversion and is much faster than currently available general inversion methods for the beta distribution. It turns out to be very useful for generating gamma processes efficiently via bridge sampling.