Mathematica's sophisticated algorithms for handling higher mathematical functions to arbitrary precision—and in symbolic form—immediately brings a new level of accuracy—and analytical capability—to statistical computation.
BetaRegularized — CDF of Student distribution
InverseBetaRegularized — quantiles of Student and beta distributions
GammaRegularized — CDF of gamma and Poisson distributions
InverseGammaRegularized — quantiles of gamma and related distributions
MarcumQ — CDF of Rice and Skellam distributions
OwenT — part of CDF of skew normal distribution