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Poisson and compound Poisson approximations in conventional and nonconventional setups
Probability Theory and Related Fields, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kifer, Yuri, Rapaport, Ariel
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Approximations for compound Poisson and Pólya processes
Advances in Applied Probability, 1985Suppose Xi≧0 are i.i.d., i = 1, 2, ···. We derive a saddlepoint approximation for P{∑N(t)k=1Xk> y} as y→∞ and t is fixed, where N(t), t≧0, is either a Poisson or a Pólya process. These results are then compared and contrasted with the well-known Esscher approximation.
Embrechts, Paul +3 more
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Stein's Method for Compound Poisson Approximation: The Local Approach
Annals of Applied Probability, 1994 In the present paper, compound Poisson approximation by Stein's method is considered. A general theorem analogous to the local approach for Poisson approximation is proved. It is then applied to a reliability problem involving the number of isolated vertices in the rectangular lattice on the torus.
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On Compound Poisson Approximations Under Moment Restrictions
Theory of Probability & Its Applications, 2000The author considers the accuracy of approximation by infinitely divisible laws with respect to the uniform and total variation distances. These results are related to the first uniform Kolmogorov theorem. As approximations the author uses compound Poisson approximations and compound Poisson measures with a sign.
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Journal of Computational Biology, 1998
We derive a Poisson process approximation for the occurrences of clumps of multiple words and a compound Poisson process approximation for the number of occurrences of multiple words in a sequence of letters generated by a stationary Markov chain. Using the Chen-Stein method, we provide a bound on the error in the approximations.
Gesine Reinert, Sophie Schbath
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We derive a Poisson process approximation for the occurrences of clumps of multiple words and a compound Poisson process approximation for the number of occurrences of multiple words in a sequence of letters generated by a stationary Markov chain. Using the Chen-Stein method, we provide a bound on the error in the approximations.
Gesine Reinert, Sophie Schbath
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Approximation of aggregate claims distributions by compound poisson distributions
Insurance: Mathematics and Economics, 1985Error estimates are given for the approximation of the individual model of risk theory by compound Poisson distributions. Theoretical portfolios and one life portfolio from practice demonstrate the quality of the estimates.
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Compound poisson approximations for the numbers of extreme spacings
Advances in Applied Probability, 1993The accuracy of the Poisson approximation to the distribution of the numbers of large and small m -spacings, when n points are placed at random on the circle, was analysed using the Stein–Chen method in Barbour et al. (1992b).
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Bulletin of Mathematical Biology, 1992
DNA and protein sequence comparisons are performed by a number of computational algorithms. Most of these algorithms search for the alignment of two sequences that optimizes some alignment score. It is an important problem to assess the statistical significance of a given score.
Goldstein, Larry, Waterman, Michael S.
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DNA and protein sequence comparisons are performed by a number of computational algorithms. Most of these algorithms search for the alignment of two sequences that optimizes some alignment score. It is an important problem to assess the statistical significance of a given score.
Goldstein, Larry, Waterman, Michael S.
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Poisson and compound Poisson approximations for random sums of random variables
Journal of Applied Probability, 1996We derive upper bounds for the total variation distance, d, between the distributions of two random sums of non-negative integer-valued random variables. The main results are then applied to some important random sums, including cluster binomial and cluster multinomial distributions, to obtain bounds on approximating them to suitable Poisson or ...
VELLAISAMY, P, CHAUDHURI, B
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Theorems of Large Deviations in the Approximation by the Compound Poisson Distribution
Acta Applicandae Mathematica, 2003A random variable \(Y\) is said to have the compound Poisson distribution if its characteristic function \(f(t)={E}e^{itY}\) is such that \[ \log f(t)= \lambda\sum_{m=1}^{N}\bigl(e^{itm}-1\bigr)p_m,\;\lambda>0,\;p_m\geq 0,\;m=1,\ldots,N,\;p_N>0,\;\sum_{m=1}^N p_m=1.
Aleškevičienė, A., Statulevičius, V.
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