Algorithm of exact computation of decomposable statistics distributions and its applications

Computationally efficient algorithm realizing exact computation 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.

Финансовая поддержка	Номер гранта
Российский научный фонд	14-50-00005
This work is supported by the Russian Science Foundation under grant No 14-50-00005.