Abstract
A Poisson binomial distribution with n possibly different success probabilities p 1, p 2,...,p n is frequently approximated by a Poisson distribution with parameter λ = p 1 + p 2 + ... + p n. LeCam’s bound p 12 + p 22 + ... + p n2 for the total variation distance between both distributions is particularly useful provided the success probabilities are small.
The paper presents an improved version of LeCam’s bound if a generalized d-dimensional Poisson binomial distribution is to be approximated by a compound Poisson distribution.
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References
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Weba, M. A note on LeCam’s bound for the distance between the Poisson binomial and the Poisson distribution. Statistical Papers 43, 445–452 (2002). https://doi.org/10.1007/s00362-002-0115-x
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DOI: https://doi.org/10.1007/s00362-002-0115-x