Аннотация:In this paper we consider the convergence of the power divergence family of statistics constructed from the multinomial distribution of degree k, to chi-squared distribution with
k-1 degrees of freedom. . In the proof we utilize known number theory results on the approximation of the number of integer points in a given set by its volume. Namely, E. Hlawka's theorem (1950) about the number of above-mentioned points in a convex set with a closed smooth boundary.
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