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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.

DOI: https://doi.org/10.4213/tvp466

Full text: PDF file (689 kB)

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

Bibliographic databases:


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
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\jour Theory Probab. Appl.
\yr 2001
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\pages 258--272
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    Citing articles on Google Scholar: Russian citations, English citations
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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
    4. Roos B., Pfeifer D., “On the distance between the distributions of random sums”, Journal of Applied Probability, 40:1 (2003), 87–106  crossref  mathscinet  zmath  isi  scopus
    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
    9. Pekoz E.A., Rollin A., Cekanavicius V., Shwartz M., “A Three–Parameter Binomial Approximation”, Journal of Applied Probability, 46:4 (2009), 1073–1085  crossref  mathscinet  zmath  isi  scopus
    10. Daskalakis C., Papadimitriou Ch.H., “On Oblivious PTAS's for Nash Equilibrium”, STOC'09: Proceedings of the 2009 ACM Symposium on Theory of Computing, 2009, 75–84  crossref  mathscinet  zmath  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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    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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    20. Cekanavicius V., “Approximation Methods in Probability Theory”, Approximation Methods in Probability Theory, Universitext, Springer International Publishing Ag, 2016, 1–274  crossref  mathscinet  isi
    21. Scarlett J., Cevher V., “Converse Bounds For Noisy Group Testing With Arbitrary Measurement Matrices”, 2016 IEEE International Symposium on Information Theory, IEEE International Symposium on Information Theory, IEEE, 2016, 2868–2872  isi
    22. Upadhye N.S., Cekanavicius V., Vellaisamy P., “On Stein Operators For Discrete Approximations”, Bernoulli, 23:4A (2017), 2828–2859  crossref  mathscinet  zmath  isi  scopus
    23. Dakduk S., ter Horst E., Santalla Z., Molina G., Malave J., “Customer Behavior in Electronic Commerce: a Bayesian Approach”, J. Theor. Appl. Electron. Commer. Res., 12:2 (2017), 1–20  crossref  isi  scopus
    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
    26. Chen X., Servedio R.A., Tan L.-YA., Waingarten E., Xie J., “Settling the Query Complexity of Non-Adaptive Junta Testing”, J. ACM, 65:6 (2018), 40  crossref  mathscinet  zmath  isi  scopus
    27. De A., Long Ph.M., Servedio R.A., “Learning Sums of Independent Random Variables With Sparse Collective Support”, 2018 IEEE 59Th Annual Symposium on Foundations of Computer Science (Focs), Annual IEEE Symposium on Foundations of Computer Science, ed. Thorup M., IEEE Computer Soc, 2018, 297–308  crossref  mathscinet  isi  scopus
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  • Теория вероятностей и ее применения Theory of Probability and its Applications
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