On using the first difference in the Stein-Chen method [PDF]
The Annals of Applied Probability, 1997 If \(X\) and \(Y\) are random variables and \(g\) a bounded Lipschitz function, then there are two natural bounds for \({\mathbf E}| g(X)- g(Y)|\), given by \(K(g)d_{\text{W}}(X,Y)\) and \(\| g\| d_{\text{TV ...
Aihua Xia
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The Stein-Chen Method, Point Processes and Compensators [PDF]
The Annals of Probability, 1992 There are two methods used for obtaining bounds on the total variation accuracy of approximation of the distribution of a sum \(N_ n\) of dependent indicators \(I_ 1,\dots,I_ n\) by a Poisson distribution. The first one [see \textit{D. Freedman}, Ann. Probab.
Barbour, A. D., Brown, Timothy C.
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Poisson Approximation Using the Stein-Chen Method and Coupling: Number of Exceedances of Gaussian Random Variables [PDF]
The Annals of Probability, 1990 Consider a family of (dependent) Gaussian random variables and count the number of them that exceed some given levels. An explicit upper bound is given for the total variation distance between the distribution of this number of exceedances and a Poisson distribution having the same mean.
Holst, Lars, Janson, Svante
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Poisson Approximation for Call Function via Stein–Chen Method
Bulletin of the Malaysian Mathematical Sciences Society, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kritsana Neammanee, Nat Yonghint
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A Note on the Distribution of the Extreme Degrees of a Random Graph Via the Stein-Chen Method [PDF]
Methodology and Computing in Applied Probability, 2023 AbstractWe offer an alternative proof, using the Stein-Chen method, of Bollobás’ theorem concerning the distribution of the extreme degrees of a random graph. Our proof also provides a rate of convergence of the extreme degree to its asymptotic distribution.
Yaakov Malinovsky
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Scanning for Clusters of Large Values in Time Series: Application of the Stein-Chen Method
Applied Mathematics, 2021 The purpose of this application paper is to apply the Stein-Chen (SC) method to provide a Poisson-based approximation and corresponding total variation distance bounds in a time series context. The SC method that is used approximates the probability density function (PDF) defined on how many times a pattern such as It,It+1,It+2 = {1 0 1} occurs ...
Tom Burr, Brad Henderson
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A Poisson Approximation for the Dirichlet Law, the Ewens Sampling Formula and the Griffiths-Engen-McCloskey Law by the Stein-Chen Coupling Method [PDF]
Bernoulli, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ulrich Hirth
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APPLICATIONS OF STEIN-CHEN METHOD FOR THE PROBLEM OF COINCIDENCES [PDF]
International Journal of Pure and Apllied Mathematics, 2017 Chanokgan Sahatsathatsana
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Extreme value theory for dependent sequences via the stein-chen method of poisson approximation
Stochastic Processes and their Applications, 1988 \textit{L. H. Y. Chen} [Ann. of Probab. 3, 534-545 (1975; Zbl 0335.60016)] extended Stein's method for obtaining error estimates in central limit approximation problems to Poisson approximations. One of the examples he considered was that of a stationary, \(\phi\)-mixing sequence of indicator random variables. In this paper, the author goes more deeply
Richard L. Smith
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Bound on Poisson approximation on the length of success runs at least k by Stein-Chen method
International Journal of Mathematical Analysis, 2019 Chanokgan Sahatsathatsana
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