RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 1983, Volume 28, Issue 4, Pages 625–636 (Mi tvp2211)  

This article is cited in 9 scientific papers (total in 9 papers)

On the accuracy of approximation of distributions of sums of independent random variables – which are nonzero with a small probability – by means of accompanying laws

A. Yu. Zaitsev

Leningrad

Abstract: Let $G_i=(1-p_i)E+p_iB_i$ where $0\le p_i\le 1$, $E$ is the distribution concentrated at zero, $B_i$ is an arbitrary one-dimensional distribution, $\displaystyle p=\max_{1\le i\le n}p_i$. Define
$$ G=\prod_{i=1}^nG_i,\qquad D=\prod_{i=1}^n\exp(G_i-E). $$
Then
$$ \sup_x|G\{(-\infty,x)\}-D\{(-\infty,x)\}|\le cp. $$


Full text: PDF file (640 kB)

English version:
Theory of Probability and its Applications, 1984, 28:4, 657–669

Bibliographic databases:

Received: 23.05.1981

Citation: A. Yu. Zaitsev, “On the accuracy of approximation of distributions of sums of independent random variables – which are nonzero with a small probability – by means of accompanying laws”, Teor. Veroyatnost. i Primenen., 28:4 (1983), 625–636; Theory Probab. Appl., 28:4 (1984), 657–669

Citation in format AMSBIB
\Bibitem{Zai83}
\by A.~Yu.~Zaitsev
\paper On the accuracy of approximation of distributions of sums of independent random variables~-- which are nonzero with a~small probability~-- by means of accompanying laws
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 4
\pages 625--636
\mathnet{http://mi.mathnet.ru/tvp2211}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=726889}
\zmath{https://zbmath.org/?q=an:0527.60026}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 4
\pages 657--669
\crossref{https://doi.org/10.1137/1128065}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984TV66700001}


Linking options:
  • http://mi.mathnet.ru/eng/tvp2211
  • http://mi.mathnet.ru/eng/tvp/v28/i4/p625

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Zaitsev, “On approximation of the sample by a Poisson point process”, J. Math. Sci. (N. Y.), 128:1 (2005), 2556–2563  mathnet  crossref  mathscinet  zmath  elib
    2. Roos B., “Kerstan's method for compound Poisson approximation”, Annals of Probability, 31:4 (2003), 1754–1771  crossref  mathscinet  zmath  isi
    3. Cekanavicius V., Wang Y.H., “Compound Poisson approximations for sums of discrete nonlattice variables”, Advances in Applied Probability, 35:1 (2003), 228–250  crossref  mathscinet  zmath  isi
    4. Roos B., “On Hipp's compound Poisson approximations via concentration functions”, Bernoulli, 11:3 (2005), 533–557  crossref  mathscinet  zmath  isi
    5. F. Götze, Yu. S. Eliseeva, A. Yu. Zaitsev, “Arak inequalities for concentration functions and the Littlewood–Offord problem”, Theory Probab. Appl., 62:2 (2018), 196–215  mathnet  crossref  crossref  mathscinet  isi  elib
    6. F. Gettse, A. Yu. Zaitsev, “Redkie sobytiya i puassonovskie tochechnye protsessy”, Veroyatnost i statistika. 26, Zap. nauchn. sem. POMI, 466, POMI, SPb., 2017, 109–119  mathnet
    7. 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
    8. Lifshits M.A. Nikitin Ya.Yu. Petrov V.V. Zaitsev A.Yu. Zinger A.A., “Toward the History of the Saint Petersburg School of Probability and Statistics. i. Limit Theorems For Sums of Independent Random Variables”, Vestnik St. Petersburg Univ. Math., 51:2 (2018), 144–163  crossref  isi
    9. F. Gettse, A. Yu. Zaitsev, “Otsenki blizosti svertok veroyatnostnykh raspredelenii na vypuklykh mnogogrannikakh”, Veroyatnost i statistika. 27, Zap. nauchn. sem. POMI, 474, POMI, SPb., 2018, 108–117  mathnet
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:118
    Full text:60
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020