A goodness-of-fit test for uniform distribution on a finite group

Abstract

Equiprobable samples with replacements from Їnite Abelian groups are con- sidered. Limit theorems are proved describing convergence of the distribution of the number of ordered subsamples meeting speciЇed linear relations to Poisson distributions. Basing on these theorems we construct a goodness-of-Їt test which checks the hypothesis on the uniform distribution of sample elements.