Computational Algorithms and Modules for the Evaluation of Statistical Distribution Functions.

This report presents a comparison of numerical methods for the evaluation of standard statistical distribution functions at with at least 10 significant digits of precision. Different series and continued fraction expansions were compared with the purpose of finding the most efficient techniques for different domains of the parameters of the Beta, Gamma, and normal distributions. Other techniques, including a Hermite expansion of exponents, a Wilson-Hilferty expansion, and asymptotic series of the Euler-McLaurin type were also investigated for extreme values of parameters. On the basis of time comparisons, the most efficient modules were combined into distribution packages. Further extensions to non-central distributions have been included in this package. Author