Statistics::distributions calculates percentage points (5 significant digits) of the u (standard normal) distribution, the student's t distribution, the chi-square distribution and the f distribution. it can also calculate the upper probability (5 significant digits) of the u (standard normal), the chi-square, the t and the f distribution. these critical values are needed to perform statistical tests, like the u test, the t test, the f test and the chi-squared test, and to calculate confidence intervals.

if you are interested in more precise algorithms you could look at:

statlib: http://lib.stat.cmu.edu/apstat/ ;

applied statistics algorithms by griffiths, p. and hill, i.d., ellis horwood: chichester (1985)