  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.
