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# Poisson approximation for random sums of Bernoulli random variables

Department of Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden
(Impact Factor: 0.53). 02/1991; DOI: 10.1016/0167-7152(91)90135-E

ABSTRACT Bounds for the total variation distance between the distribution of the sum of a random number of Bernoulli summands and an appropriate Poisson distribution are given. The results can be used to derive limit theorems with rates of convergence for marked and thinned point processes. Some examples are given.

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• "Let λ N = N i=1 p i , λ = E(λ N ) and U λ a Poisson random variable with mean λ. For approximating the distribution of S N by a Poisson distribution with mean λ, Yannaros [2] gave a bound for the total variation "
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08/2014; 94(5). DOI:10.12732/ijpam.v94i5.6
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• "K. Teerapabolarn random variable with mean λ. For approximating the distribution of S N by a Poisson distribution with mean λ in the point metric form, Yannaros [8] gave a bound in the form of "
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• "In this study, non-uniform and uniform bounds for the distance between the distribution function of random sums of independent Bernoulli random variables and an appropriate Poisson distribution function were improved. They are sharper than those reported in [8] and [2]. "
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11/2013; 89(1). DOI:10.12732/ijpam.v89i1.4