A self-validating numerical method for computation of central and non-central F probabilities and percentiles

A self-validating numerical method based on interval analysis for the computation of central and non-central F probabilities and percentiles is reported. The major advantage of this approach is that there are guaranteed error bounds associated with the computed values (or intervals), i.e. the computed values satisfy the user-specified accuracy requirements. The methodology reported in this paper can be adapted to approximate the probabilities and percentiles for other commonly used distribution functions.