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Compound Poisson approximation: a user's guide [PDF]
Annals of Applied Probability, 2001 Compound Poisson approximation is a useful tool in a variety of applications, including insurance mathematics, reliability theory, and molecular sequence analysis. In this paper, we review the ways in which Stein’s method can currently be used to derive bounds on the error in such approximations.
A D Barbour
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Approximation by the Compound Poisson Law
Theory of Probability & Its Applications, 2005Summary: We consider a specification of the convergence of distributions of sums of independent, nonnegative integer random variables to the compound Poisson distribution. Theorems of large deviations and asymptotic expansions under some weak conditions are proved.
Aleškevičiėnė, A. K. +1 more
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COMPARISON OF APPROXIMATIONS FOR COMPOUND POISSON PROCESSES
ASTIN Bulletin, 2015AbstractIn this paper, we compare the error in several approximation methods for the cumulative aggregate claim distribution customarily used in the collective model of insurance theory. In this model, it is usually supposed that a portfolio is at risk for a time period of length t.
Choirat, C., SERI, RAFFAELLO
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Compound Poisson approximation in total variation
Stochastic Processes and Their Applications, 1999 Poisson approximation in total variation can be successfully established in a wide variety of contexts, involving sums of weakly dependent random variables which usually take the value 0, and occasionally the value 1. If the random variables can take other positive integer values, or if there is stronger dependence between them, compound Poisson ...
A D Barbour
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Compound Poisson Approximation to Convolutions of Compound Negative Binomial Variables
Methodology and Computing in Applied Probability, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Neelesh S Upadhye, P Vellaisamy
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On Compound Poisson Approximation for Sequence Matching
Combinatorics, Probability and Computing, 2000Consider sequences {Xi}mi=1 and {Yj}nj=1 of independent random variables, taking values in a finite alphabet, and assume that the variables X1, X2, … and Y1, Y2, … follow the distributions μ and v, respectively. Two variables Xi and Yj are said to match if Xi = Yj.
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Stein's method for Poisson and compound Poisson approximation
Lecture Notes Series, Institute for Mathematical Sciences, 2005exaly +2 more sources
LARGE DEVIATIONS FOR SIGNED COMPOUND POISSON APPROXIMATIONS
Statistics & Risk Modeling, 1997The authors introduce large deviations for signed compound Poisson measures with compounding asymptotic expansions. The main common property for such deviations is the enlargement of the equivalence zone for probabilities and tails in comparison with Poisson and normal approximations.
Čekanavičius, Vydas, Vaitkus, Pranas
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Stein’s method for conditional compound Poisson approximation
Statistics & Probability Letters, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gan, H. L., Xia, A.
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On magic factors in Stein’s method for compound Poisson approximation
Electronic Communications in Probability, 2017 12 ...
Fraser Daly
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