On the computation and inversion of the cumulative noncentral beta distribution function
This work provides practical numerical tools for statisticians and applied researchers who need to compute or invert the noncentral beta distribution, though it is an incremental improvement over existing methods.
The paper addresses the stable computation and inversion of the noncentral beta distribution function, providing asymptotic expansions for large parameters and approximations for inversion that serve as starting points for iterative methods.
The computation and inversion of the noncentral beta distribution $B_{p,q}(x,y)$ (or the noncentral $F$-distribution, a particular case of $B_{p,q}(x,y)$) play an important role in different applications. In this paper we study the stability of recursions satisfied by $B_{p,q}(x,y)$ and its complementary function and describe asymptotic expansions useful for computing the function when the parameters are large. We also consider the inversion problem of finding $x$ or $y$ when a value of $B_{p,q}(x,y)$ is given. We provide approximations to $x$ and $y$ which can be used as starting values of methods for solving nonlinear equations (such as Newton) if higher accuracy is needed.