1999
DOI: 10.1007/bf02465531
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Large deviations for integer centered poisson approximation

Abstract: Abstract. Large deviations in a centered Poisson approximation are examined. For lattice distributions, the centered Poisson approximation is more universal than the normal and standard Poisson laws.

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Cited by 3 publications
(6 citation statements)
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“…We have used the negative binomial approximation, which takes care of two matching moments, while the Poisson approximation matches only the mean. For independent summands, the same effect in LD has been achieved, when the Poisson approximation was replaced by a shifted Poisson law, see [4].…”
Section: Resultsmentioning
confidence: 72%
“…We have used the negative binomial approximation, which takes care of two matching moments, while the Poisson approximation matches only the mean. For independent summands, the same effect in LD has been achieved, when the Poisson approximation was replaced by a shifted Poisson law, see [4].…”
Section: Resultsmentioning
confidence: 72%
“…The integer-centered Poisson law was introduced in [24]. Other results can be found in [14], [16]. 1-I c is not a unique discrete measure possessing such properties (see [14], [15], [24], [25]); however, it is the most simply structured one.…”
Section: Integral and Local Estimatesmentioning
confidence: 98%
“…All these parameters are expressible in terms of h and characteristics of F. On the other hand, we are free in choosing z and parameters of D as long as (3.7) is fulfilled. As is noted in [16], the most difficult part is the estimation of A2(x). Therefore, we set z = h. Then A2 = 0 and…”
Section: D= Fi Cmentioning
confidence: 98%
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