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Efficient computation for the Poisson binomial distribution

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Abstract

Direct construction of the probability distribution function for a Poisson binomial random variable, where success probabilities may vary from trial to trial, requires on the order of \(2^{n}\) calculations, and is computationally infeasible for all but modest sized problems. An approach offered by Thomas and Taub (J Stat Comput Simul 14:125–131 1982) reduces this effort to approximately \(n^{2}\), which, while certainly an improvement, can still be significant for large values of \(n\). We offer modifications to the method of Thomas and Taub that greatly reduce the computations while still delivering highly accurate results.

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Authors and Affiliations

  1. Department of Information Systems, Statistics, and Management Science, University of Alabama, Tuscaloosa, AL , 35487, USA

    Bruce E. Barrett & J. Brian Gray

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  1. Bruce E. Barrett
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  2. J. Brian Gray
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Correspondence to Bruce E. Barrett.

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Barrett, B.E., Gray, J.B. Efficient computation for the Poisson binomial distribution. Comput Stat 29, 1469–1479 (2014). https://doi.org/10.1007/s00180-014-0501-6

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  • DOI: https://doi.org/10.1007/s00180-014-0501-6

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