An application of a multivariate central limit theorem to sampling without replacement
A general multivariate central limit theorem of \textit{M. G. Hahn}, \textit{P. Hahn}, and \textit{M. J. Klass} [Ann. Probab. 11, 277-301 (1983; Zbl 0514.60025)] gives conditions relating the one-dimensional marginals of the summands in an infinitesimal triangular array to those of the limit law. This theorem is applied here to the sample sums obtained by sampling without replacement from a sequence of finite multivariate populations. An important subcase of this result is where the sequence of populations' values are restricted to a finite set. Here the limit laws are shown to be a natural generalization of the multivariate Poisson distribution.
generalized multivariate hypergeometric distribution
sequence of finite multivariate populations
generalization of the multivariate Poisson distribution
scientific article; zbMATH DE number 4074177
scientific article