  The implementation of Bayesian predictive procedures under standard normal
models is considered. Two distributions are of particular interest, the K-prime
and K-square distributions. They also give exact inferences for simple and
multiple correlation coefficients. Their cumulative distribution functions can
be expressed in terms of infinite series of multiples of incomplete beta
function ratios, thus adequate for recursive calculations. Efficient algorithms
are provided. To deal with special cases where possible underflows may prevent
a recurrence to work properly, a simple solution is proposed which results in a
procedure which is intermediate between two classes of algorithm. Some examples
of applications are given.
