On a statistic for testing the homogeneity of polynomial samples

摘要

We consider M ≥ 2 independent polynomial samples with N outcomes. For the case when M and N are fixed but sizes of samples tend to infinity we find limit distributions of a new statistic σ~2: chi-square distribution with (M-1)(N-1) degrees of freedom if samples are statistically homogeneous, non-central chisquare distribution with the same number of degrees of freedom if samples are ?convergent? to homogeneous ones, and normal distribution if samples are statistically nonhomogeneous.