The computation and inversion of the noncentral beta distribution Bp,q(x, y) (or the noncentral F-distribution, a particular case of Bp,q(x, y)) play an important role in different applications. In this paper we study the stability of recursions satisfied by Bp,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 Bp,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.

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Applied Mathematics and Computation
Scientific Computing

Gil, A., Segura, J., & Temme, N. (2019). On the computation and inversion of the cumulative noncentral beta distribution function. Applied Mathematics and Computation, 361, 74–86. doi:10.1016/j.amc.2019.05.014