Accurate Computation of the F-to-z and t-to-z Transforms for Large Arguments

Abstract

The obvious method for transforming an F or t variate into a z variate is via the corresponding p value, but this method is inaccurate when F or t is so large that p differs from 1 by only the last few bits of its floating-point representation. More accurate results may be obtained by using q = 1 - p as the intermediate variable so that the full precision of the floating-point representation is available.