Аннотация:Computationally efficient algorithm realizing exact compu-
tation of decomposable statistics distributions for multinomial scheme
is described. The algorithm is based on the embedding the scheme into
nonhomogeneous Markov chain. It was used to compute the Pearson
statistics distribution and distributions of some statistics for the random
allocation of particles into cells. Comparisons of exact numerical values
of distribution functions of statistics with usually used approximations
from corresponding limit theorems show that exact tail probabilities may
be considerably larger than that of approximating distributions.