On signed normal-Poisson approximations

For lattice distributions a convolution of two signed Poisson measures proves to be an approximation comparable with the normal law. It enables to get rid of cumbersome summands in asymptotic expansions and to obtain estimates for all Borel sets. Asymptotics can be constructed two-ways: by adding su...

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Bibliographic Details
Published in:Probability theory and related fields 1998-08, Vol.111 (4), p.565-583
Main Author: CEKANAVICIUS, V
Format: Article
Language:English
Subjects:
Approximation
Asymptotic series
Borel sets
Exact sciences and technology
Mathematics
Probability
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Stochastic processes
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Summary:For lattice distributions a convolution of two signed Poisson measures proves to be an approximation comparable with the normal law. It enables to get rid of cumbersome summands in asymptotic expansions and to obtain estimates for all Borel sets. Asymptotics can be constructed two-ways: by adding summands to the leading term or by adding summands in its exponent. The choice of approximations is confirmed by the Ibragimov-type necessary and sufficient conditions.
ISSN:0178-8051
1432-2064
DOI:10.1007/s004400050178