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Teor. Veroyatnost. i Primenen., 2000, Volume 45, Issue 2, Pages 328–344 (Mi tvp466)  

This article is cited in 28 scientific papers (total in 28 papers)

Binomial approximation to the Poisson binomial distribution: The Krawtchouk expansion

B. Roos

Institut für Mathematische Stochastik, Universität, Germany

Abstract: The Poisson binomial distribution is approximated by a binomial distribution and also by finite signed measures resulting from the corresponding Krawtchouk expansion. Bounds and asymptotic relations for the total variation distance and the point metric are given.

Keywords: binomial approximation, Poisson binomial distribution, Krawtchouk expansion, signed measures, total variation distance, point metric.


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English version:
Theory of Probability and its Applications, 2001, 45:2, 258–272

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Citation: B. Roos, “Binomial approximation to the Poisson binomial distribution: The Krawtchouk expansion”, Teor. Veroyatnost. i Primenen., 45:2 (2000), 328–344; Theory Probab. Appl., 45:2 (2001), 258–272

Citation in format AMSBIB
\by B.~Roos
\paper Binomial approximation to the Poisson binomial distribution: The Krawtchouk expansion
\jour Teor. Veroyatnost. i Primenen.
\yr 2000
\vol 45
\issue 2
\pages 328--344
\jour Theory Probab. Appl.
\yr 2001
\vol 45
\issue 2
\pages 258--272

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    This publication is cited in the following articles:
    1. Choi K.P., Xia A.H., “Approximating the number of successes in independent trials: Binomial versus Poisson”, Annals of Applied Probability, 12:4 (2002), 1139–1148  crossref  mathscinet  zmath  isi  scopus
    2. Roos B., “Kerstan's method for compound Poisson approximation”, Annals of Probability, 31:4 (2003), 1754–1771  crossref  mathscinet  zmath  isi  scopus
    3. Roos B., “Improvements in the Poisson approximation of mixed Poisson distributions”, Journal of Statistical Planning and Inference, 113:2 (2003), 467–483  crossref  mathscinet  zmath  isi  scopus
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    5. Cekanavicius V., Roos B., “Compound binomial approximations”, Annals of the Institute of Statistical Mathematics, 58:1 (2006), 187–210  crossref  mathscinet  zmath  isi  scopus
    6. Cekanavicius V., Roos B., “Binomial approximation to the Markov binomial distribution”, Acta Applicandae Mathematicae, 96:1–3 (2007), 137–146  crossref  mathscinet  zmath  isi  scopus
    7. Adell J.A., Anoz J.M., “Signed binomial approximation of binomial mixtures via differential calculus for linear operators”, Journal of Statistical Planning and Inference, 138:12 (2008), 3687–3695  crossref  mathscinet  zmath  isi  scopus
    8. Niu R., Varshney P.K., “Performance analysis of distributed detection in a random sensor field”, IEEE Transactions on Signal Processing, 56:1 (2008), 339–349  crossref  mathscinet  zmath  adsnasa  isi  scopus
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    12. Theory Probab. Appl., 57:1 (2013), 97–109  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. Skipper M., “A Polya Approximation to the Poisson-Binomial Law”, J. Appl. Probab., 49:3 (2012), 745–757  crossref  mathscinet  zmath  isi  scopus
    14. Daskalakis C. Papadimitriou Ch., “Sparse Covers For Sums of Indicators”, Probab. Theory Relat. Field, 162:3-4 (2015), 679–705  crossref  mathscinet  zmath  isi  scopus
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    16. Roos B., “on Bobkov'S Approximate de Finetti Representation Via Approximation of Permanents of Complex Rectangular Matrices”, Proc. Amer. Math. Soc., 143:4 (2015), PII S0002-9939(2014)12429-4, 1785–1796  crossref  mathscinet  zmath  isi  scopus
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    18. De A., “Beyond the Central Limit theorem: Asymptotic Expansions and Pseudorandomness for Combinatorial Sums”, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS) (Berkeley, CA, USA), IEEE, 2015, 883–902  crossref  mathscinet  isi  scopus
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    24. Biscarri W. Zhao S.D. Brunner R.J., “A Simple and Fast Method For Computing the Poisson Binomial Distribution Function”, Comput. Stat. Data Anal., 122 (2018), 92–100  crossref  mathscinet  isi  scopus
    25. Mossel E., Neeman J., Sly A., “A Proof of the Block Model Threshold Conjecture”, Combinatorica, 38:3 (2018), 665–708  crossref  mathscinet  zmath  isi  scopus
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  • Теория вероятностей и ее применения Theory of Probability and its Applications
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