# zbMATH — the first resource for mathematics

The rate of convergence to the normal law for sampling without replacement. (Russian) Zbl 0574.60028
Let $$(\nu_{\ell 1},...,\nu_{\ell m})$$ be a random Boolean vector, where $$\nu_{\ell m}=1$$ if the m-th element of a finite population of volume N is chosen in the l-th sampling of volume $$n_{\ell}$$ $$(\ell =1,...,s)$$, and $$\nu_{\ell m}=0$$ otherwise, $$m=1,...,N$$, $$\nu_{\ell 1}+...+\nu_{\ell N}=n_{\ell}$$, $$\ell =1,...,s$$. Let $$f_{jm}^{(N)}(x_ 1,...,x_ s)$$ be a random function of a Boolean vector $$(x_ 1,...,x_ s)$$, $$j=1,...,k$$; $$m=1,...,N$$, and $$S_{jN}=\sum^{N}_{m=1}f_{jm}^{(N)}(\nu_{1m},..,\nu_{sm})$$, $$j=1,...,k$$. The rate of convergence of order 1/$$\sqrt{N}$$ to a multidimensional normal law is proved for a vector $$(S_{1N},...,S_{kN})$$.
Reviewer: N.Leonenko

##### MSC:
 60F05 Central limit and other weak theorems 60C05 Combinatorial probability