Algorithms for the inversion of the noncentral beta distribution function

Abstract Two distinct algorithms are presented to address inversion problems associated with the noncentral beta distribution function, $$B_{p,q}(x,y)$$ . These algorithms correspond to two types of inversion: a) Inversion with respect to x : in this case, the noncentrality parameter of the distribution function is estimated. b) Inversion with respect to y : here, the goal is to compute the quantiles of the noncentral beta distribution. The algorithms combine asymptotic approximations–used to estimate initial values when applicable–with efficient iterative methods for solving the resulting nonlinear equations. Extensive testing indicates that our algorithms (implemented in Matlab) outperform existing implementations and, in the case of the algorithm for computing the noncentrality parameter, fills a gap in current mathematical software libraries.