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The Poisson approximation for the number of matches of values of a discrete function on segments of a sequence of random variables
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A. M. Shoitov
Published/Copyright:
May 1, 2005
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
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Articles in the same Issue
- A power divergence test in the problem of sample homogeneity for large numbers of outcomes and trials
- The Poisson approximation for the number of matches of values of a discrete function on segments of a sequence of random variables
- A theorem on probabilities of large deviations for decomposable statistics which do not satisfy the Cramér condition
- An upper bound for the number of functions satisfying the strict avalanche criterion
- Adjustment experiments for automata with variable logic of behaviour
- Equational closure
- Criteria for a Boolean function to be a repetition-free in the pre-elementary bases of rank 3
- On the length of checking test for repetition-free functions in the basis {0, 1, &, ∨, ¬}
- Touchard C-polynomials and quasi-orthogonal to them polynomials
