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Journal of Theoretical ProbabilityAbstractThe problem of evaluating the accuracy of Poisson approximation to the distribution of a sum of independent integer-valued random variables has attracted a lot of attention in the past six decades. Among authors who contributed to the topic are Prokhorov, Kolmogorov, LeCam, Shorgin, Barbour, Hall, Deheuvels, Pfeifer, Roos, and many others. From
S. Novak
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Karpatsʹkì Matematičnì Publìkacìï, 2022 In the paper, we investigate an asymptotic behavior of the sharp upper bounds in the integral metric of deviations of the Abel-Poisson integrals from functions from the class $L^{\psi}_{\beta, 1}$.
T.V. Zhyhallo, Yu.I. Kharkevych
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Probability Surveys, 2005 We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well.
S.Y.Novak
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Compound Poisson Approximation via Information Functionals [PDF]
Electronic Journal of Probability, 2010 An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of independent integer-valued random variables $Y_i$.
Barbour, AD +3 more
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Asymptotics of approximation of functions by conjugate Poisson integrals
Karpatsʹkì Matematičnì Publìkacìï, 2020 Among the actual problems of the theory of approximation of functions one should highlight a wide range of extremal problems, in particular, studying the approximation of functional classes by various linear methods of summation of the Fourier series. In
I.V. Kal'chuk +2 more
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Poisson Approximation for Dependent Trials
The Annals of Probability, 1975 Let $X_1, \cdots, X_n$ be an arbitrary sequence of dependent Bernoulli random variables with $P(X_i = 1) = 1 - P(X_i = 0) = p_i.$ This paper establishes a general method of obtaining and bounding the error in approximating the distribution of $\sum^n_{i=1} X_i$ by the Poisson distribution.
Louis H. Y. Chen
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Disagreement coupling of Gibbs processes with an application to Poisson approximation [PDF]
The Annals of Applied Probability, 2021 We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach in Hofer-Temmel (2019) and Hofer-Temmel and Houdebert (2019) we will use this to couple two finite Gibbs ...
G. Last, M. Otto
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Improvements of Poisson approximation for n-dimensional unit cube random graph [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2021 This paper uses the Stein-Chen method to obtain uniform and non-uniform bounds in the Poisson approximation for the n-dimensional unit cube random graph. These bounds are re-established under the restriction of Poisson mean λ = 1.
Kanint Teerapabolarn
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Poisson Approximation to the Convolution of Power Series Distributions [PDF]
Probability and Mathematical Statistics, 2020 In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions.
Amit Kumar, P. Vellaisamy, F. Viens
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Monotonicity properties of the Poisson approximation to the binomial distribution [PDF]
Statistics and Probability Letters, 2020 Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate) tests of hypotheses on an unknown value of the parameter p of the ...
I. Pinelis
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