  The computation of two Bayesian predictive distributions which are discrete
mixtures of incomplete beta functions is considered. The number of iterations
can easily become large for these distributions and thus, the accuracy of the
result can be questionable. Therefore, existing algorithms for that class of
mixtures are improved by introducing round-off error calculation into the
stopping rule. A further simple modification is proposed to deal with possible
underflows that may prevent recurrence to work properly.
