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We find conditions which are sufficient for convergence of the distribution of the number of matches of values of a function considered on tuples of arguments taken from a sequence of independent identically distributed random variables to the Poisson law and estimate the convergence rate. We derive a series of corollaries of this result. In particular, in the equiprobable polynomial scheme we obtain Poisson limit theorems for the number of pairs of non-overlapping tuples with identical frequencies of occurrences of symbols and for the number of pairs of tuples with identical structure.
Published Online: 2005-05-01
Published in Print: 2005-05-01
Copyright 2005, Walter de Gruyter
