Evaluation of Some Cumulative Distribution Functions by Numerical Quadrature

Integral representations of several statistical distributions are exploited in a common structure to guarantee significant digit results over wide ranges of parameters. Truncation errors are estimated from computed results and computational problems arising from extreme parameters are identified. Central distributions are treated implicitly by setting noncentrality parameters to zero. Bounds analogous to those for Mill’s ratio are also given for some nonnegative special functions.