Exact algorithms for computing p-values of statistics-linear combination of 3-nomial variables

Algorithms for computing exact distribution values of statistics-linear combination of some multinomial variables called 3-nomial variables are derived. In the general case, there are no explicit formulae of the cumulative distribution function of these statistics that allow the direct computation of pp-values. The exact distribution in the independent case and in some dependent ones is studied. For each of the two cases of dependence, an algorithm based on recursive relationships is proposed, giving the number of favorable cases and combinatorics to minimize computation time. For each of these NFC algorithms, concurrent PGF algorithms and some realized comparisons are presented.