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Teoriya Veroyatnostei i ee Primeneniya, 1977, Volume 22, Issue 4, Pages 867–871 (Mi tvp3637)  

This article is cited in 36 scientific papers (total in 36 papers)

Short Communications

Approximation of a generalized binomial distribution

S. Ya. Šorgin

Moscow
Abstract: The distribution of
\begin{gather*} S_n=X_1+\dots+X_n \\ (\mathbf P\{X_j=1\}=p_j,\quad\mathbf P\{X_j=0\}=1-p_j) \end{gather*}
is investigated. Some results are obtained concerning the rate of its convergence to a Poisson law and to some modifications of the Poisson law.
Received: 14.07.1976
English version:
Theory of Probability and its Applications, 1978, Volume 22, Issue 4, Pages 846–850
DOI: https://doi.org/10.1137/1122099
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. Ya. Šorgin, “Approximation of a generalized binomial distribution”, Teor. Veroyatnost. i Primenen., 22:4 (1977), 867–871; Theory Probab. Appl., 22:4 (1978), 846–850
Citation in format AMSBIB
\Bibitem{Sho77}
\by S.~Ya.~{\v S}orgin
\paper Approximation of a~generalized binomial distribution
\jour Teor. Veroyatnost. i Primenen.
\yr 1977
\vol 22
\issue 4
\pages 867--871
\mathnet{http://mi.mathnet.ru/tvp3637}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=458544}
\zmath{https://zbmath.org/?q=an:0392.60021}
\transl
\jour Theory Probab. Appl.
\yr 1978
\vol 22
\issue 4
\pages 846--850
\crossref{https://doi.org/10.1137/1122099}
Linking options:
  • https://www.mathnet.ru/eng/tvp3637
  • https://www.mathnet.ru/eng/tvp/v22/i4/p867
  • This publication is cited in the following 36 articles:
    1. S. Y. Novak, “On Poisson Approximation”, J Theor Probab, 2024  crossref
    2. José A. Adell, “Explicit upper bounds for the Stirling numbers of the first kind”, Journal of Combinatorial Theory, Series A, 192 (2022), 105669  crossref
    3. Cekanavicius V. Vellaisamy P., “Compound Poisson Approximations in l(P)-Norm For Sums of Weakly Dependent Vectors”, J. Theor. Probab., 34:4 (2021), 2241–2264  crossref  isi
    4. Dumitru Popa, “The Korovkin Parabola Envelopes Method and Voronovskaja-Type Results”, Mediterr. J. Math., 18:4 (2021)  crossref
    5. Emanuele Dolera, Stefano Favaro, “A Berry–Esseen theorem for Pitman's $\alpha $-diversity”, Ann. Appl. Probab., 30:2 (2020)  crossref
    6. S. Y. Novak, “Poisson approximation”, Probab. Surveys, 16:none (2019)  crossref
    7. S. Y. Novak, “On the accuracy of Poisson approximation”, Extremes, 22:4 (2019), 729  crossref
    8. I. G. Shevtsova, “Convergence rate estimates in the global CLT for compound mixed Poisson distributions”, Theory Probab. Appl., 63:1 (2018), 72–93  mathnet  crossref  crossref  isi  elib
    9. Ron Goldman, Xiao-Wei Xu, Xiao-Ming Zeng, “Applications of the Shorgin Identity to Bernstein Type Operators”, Results Math, 73:1 (2018)  crossref
    10. Kruopis J. Cekanavicius V., “Compound Poisson Approximations for Symmetric Vectors”, J. Multivar. Anal., 123 (2014), 30–42  crossref  isi
    11. C&H/CRC Monographs on Statistics & Applied Probability, 20114852, Extreme Value Methods with Applications to Finance, 2011, 351  crossref
    12. Zacharovas V., Hwang H.-K., “A Charlier–Parseval Approach to Poisson Approximation and its Applications”, Lithuanian Mathematical Journal, 50:1 (2010), 88–119  crossref  mathscinet  zmath  isi
    13. Theory Probab. Appl., 55:2 (2011), 198–224  mathnet  crossref  crossref  mathscinet  isi
    14. V. Čekanavičius, B. Roos, “An expansion in the exponent for compound binomial approximations”, Lith Math J, 46:1 (2006), 54  crossref
    15. D. N. Karymov, “On the accuracy of approximation in the Poisson limit theorem”, Discrete Math. Appl., 14:3 (2004), 317–327  mathnet  crossref  crossref  mathscinet  zmath
    16. 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
    17. Roos B., “Sharp constants in the Poisson approximation”, Statistics & Probability Letters, 52:2 (2001), 155–168  crossref  mathscinet  zmath  isi
    18. P. Harremoes, “Binomial and Poisson distributions as maximum entropy distributions”, IEEE Trans. Inform. Theory, 47:5 (2001), 2039  crossref
    19. B. Roos, “Multinomial and Krawtchouk Approximations to the Generalized Multinomial Distribution”, Theory Probab. Appl., 46:1 (2002), 103–117  mathnet  mathnet  crossref  crossref  isi
    20. A.D. Barbour, Handbook of Statistics, 19, Stochastic Processes: Theory and Methods, 2001, 79  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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