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Lithuanian Mathematical Journal

, Volume 37, Issue 1, pp 1–12 | Cite as

Approximation of the generalized Poisson binomial distribution: Asymptotic expansions

  • V. Čekanavičius
Article

Keywords

Asymptotic Expansion Binomial Distribution Independent Random Variable Triangular Function Uniform Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    T. V. Arak and A. Yu. Zaitsev, Uniform limit theorems for sums of independent random variables,Proc. Steklov Inst. Math.,174, 1–222 (1988).MathSciNetGoogle Scholar
  2. 2.
    A. D. Barbour and P. Hall, On the rate of Poisson convergence,Math. Proc. Cambridge Philos. Soc.,95, 473–480 (1984).zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    H. Bergström, On asymptotic expansion of probability functions,Skand. Aktuarietidskrift,1, 1–34 (1951).zbMATHGoogle Scholar
  4. 4.
    V. Čekanavičius, Lower bound in the Bergström identity,Liet. Matem. Rink.,28, 153–169 (1988).zbMATHGoogle Scholar
  5. 5.
    V. Čekanavičius, Approximation by accompanying distributions and asymptotic expansions. I,Lith. Math. J.,29, 75–80 (1989).CrossRefzbMATHGoogle Scholar
  6. 6.
    V. Čekanavičius, On multivariate Le Cam theorem and compound Poisson measures,Statist. Probab. Lett.,25, 145–151 (1995).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    L. H. Y. Chen and M. Roos. Compound Poisson approximation for unbounded functions on a group with application to large deviations,Probab. Theory Relat. Fields,103, 515–528 (1995).zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    R. Cuppens,Decompositon of Multivariate Probability, Academic Press, New York-San Francisco-London (1975).Google Scholar
  9. 9.
    P. Deheuvels and D. Pfeifer, Poisson approximation of multinomial distributions and point processes,J. Multivariate Anal.,25, 65–89 (1988).zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    U. Gerber, Error bounds for the compound Poisson approximation,Insurance: Mathematics and Economics,3, 191–194 (1984).zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    C. Hipp, Approximation of aggregate claims distributions by compound Poisson distributions,Insurance: Mathematics and Economics,4, 227–232 (1985).zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    C. Hipp, Improved approximations for the aggregate claims distribution in the individual model,ASTIN Bull.,16, 89–100 (1987).CrossRefGoogle Scholar
  13. 13.
    P. Kornya, Distribution of aggregate claims in the Individual Risk Theory model,Society of Actuaries: Transactions,35, 823–858 (1983).Google Scholar
  14. 14.
    J. Kruopis, Precision of approximations of the generalized binomial distribution by convolutions of Poisson measures,Lith. Math. J.,26, 37–49 (1986).zbMATHCrossRefGoogle Scholar
  15. 15.
    L. Le Cam, An approximation theorem for the Poisson binomial distribution,Pacific J. Math.,10, 1181–1197 (1960).zbMATHMathSciNetGoogle Scholar
  16. 16.
    L. Le Cam, On the distribution of sums of independent random variables, in:Bernoulli, Bayes, Laplace (Anniversary volume), Springer-Verlag, Berlin-Heidelberg-New York (1965), pp. 179–202.Google Scholar
  17. 17.
    R. Michel, An improved error bound for the compound Poisson approximation of a nearly homogeneous portfolio,ASTIN Bull.,17, 165–169 (1988).CrossRefGoogle Scholar
  18. 18.
    S. V. Nagaev and V. I. Chebotarev, On asymptotic expansions of Bergström type in Hilbert space,Trudy Inst. Mat. (Novosibirsk),13, 66–77 (1989).zbMATHMathSciNetGoogle Scholar
  19. 19.
    E. L. Presman, Approximation of binomial distributions by infinitely divisible ones,Theory Probab. Appl.,28, 393–403 (1983).MathSciNetCrossRefGoogle Scholar
  20. 20.
    E. L. Presman, The variation distance between the distribution of a sum of independent Bernoulli variables and the Poisson law,Theory Probab. Appl.,30, 417–422 (1985).MathSciNetCrossRefGoogle Scholar
  21. 21.
    S. T. Rachev and L. Rüschendorf, Approximation of sums by compound Poisson distributions with respect to stop-loss distances,Adv. Appl. Probab.,22, 350–374 (1990).zbMATHCrossRefGoogle Scholar
  22. 22.
    J. Šiaulys and V. Čekanavičius, Approximation of distributions of integer-valued additive functions by discrete charges. II,Lith. Math. J.,29, 80–95 (1989).CrossRefzbMATHGoogle Scholar
  23. 23.
    Y. H. Wang, From Poisson to compound Poisson approximations,Math. Sci.,14, 38–49 (1989).zbMATHMathSciNetGoogle Scholar
  24. 24.
    A. Yu. Zaitsev, On the accuracy of approximation of distributions of sums of independent random variables-which are nonzero with a small probability by accompanying laws,Theory Probab. Appl.,28, 657–664 (1984).CrossRefGoogle Scholar
  25. 25.
    A. Yu. Zaitsev, On the uniform approximation of functions of the distribution of sums of independent random variables,Theory Probab. Appl.,32, 40–47 (1987).CrossRefGoogle Scholar
  26. 26.
    A. Yu. Zaitsev, A multidimensional variant of Kolmogorov's second uniform limit theorem,Theory Probab. Appl.,34, 108–128 (1989).MathSciNetCrossRefGoogle Scholar

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© Plenum Publishing Corporation 1997

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  • V. Čekanavičius

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