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On the accuracy of approximation in the Poisson limit theorem
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D. N. Karymov
Published/Copyright:
July 1, 2004
In this paper, we find non-uniform bounds in the Poisson theorem. Let I1, ..., In be indicators of independent random events. We set pk = P{Ik = 1} = 1 − P{Ik = 0}, 0 ≤ pk ≤ 1, k = 1, ..., n. Let
Let bk be the jump of the distribution function B(x) at the point k. We also set
Let
be the jumps of the Poisson distribution function with parameter λ ≥ 0, and let
be the corresponding distribution function.
An example of the results obtained in the paper is formulated as follows. For λ = nP1 and k ≥ 2 + λ,
and for k > 1 + λe
Published Online: 2004-07-01
Published in Print: 2004-07-01
Copyright 2004, Walter de Gruyter
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Articles in the same Issue
- On the number of closure-type mappings
- Spectral properties of a linear congruent generator in special cases
- On the key space of the McEliece cryptosystem based on binary Reed–Muller codes
- On the complexity of polarised polynomials of multi-valued logic functions in one variable
- Simulation of circuits of functional elements by the universal Turing machine
- Implementation of Markov chains over Galois fields
- On solving automaton equations
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