MPROB: Computation of multinomial probabilities

An algorithm for computing exact multinomial probabilities is presented that uses the fewest number of operations that are possible without symbolic simplification of the multinomial coefficient and performs them in a sequence that minimizes the potential for overflow or underflow errors. Multinomial probabilities computed with this algorithm are accurate to machine precision, unlike those based on logarithmic transformations and/or the evaluation of factorials, using Stirling’s approximation.