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Asymptotic expansions for compound Poisson measures

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References

  1. T. V. Arak, Approximation of n-fold convolutions of distributions, having a nonnegative characteristics function by accompanying laws,Theory Probab. Appl.,25, 221–243 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  2. T. V. Arak and A. Yu. Zaitsev, Uniform limit theorems for sums of independent random variables,Proc. Steklov Inst. Math.,174, 1–222 (1988).

    MathSciNet  Google Scholar 

  3. A. D. Barbour, L. H. Y. Chen and W.-L. Loh, Compound Poisson approximation for nonnegative random variables via Stein’s method,Ann. Probab.,20, 1843–1866 (1992).

    MATH  MathSciNet  Google Scholar 

  4. H. Bergström, On asymptotic expansion of probability functions,Scand. Aktuar.,1, 1–34 (1951).

    MATH  Google Scholar 

  5. A. Bikelis and J. Mogyoròdi, Asymptotic expansions forn-fold convolutions ofk-dimensional distributions,Liet. Mat. Rinkinys,10, 433–443 (1970).

    MATH  Google Scholar 

  6. J. G. Booth, P. Hall and A. T. A. Wood, On the validity of Edgeworth and saddlepoint approximations,J. Multivariate Anal.,51, 121–138 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  7. V. Čekanavičius, Approximation by accompanying distributions and asymptotic expansions I,Lith. Math. J.,29, 75–80 (1989).

    Article  Google Scholar 

  8. V. Čekanavičius, Approximation of mixtures of distributions,Lith. Math. J.,31, 243–257 (1991).

    Article  Google Scholar 

  9. V. Čekanavičius, On asymptotic expansions in the first uniform Kolmogorov theorem,Statist. Probab. Lett.,25, 145–151 (1995).

    Article  MathSciNet  Google Scholar 

  10. V. Čekanavičius, On multivariate Le Cam theorem and compound Poisson measures,Statist. Probab. Lett.,28, 33–39 (1996).

    Article  MathSciNet  Google Scholar 

  11. L. H. Y. Chen and M. Roos, Compound Poisson approximation for unbounded functions on a group with application to large deviations,Probab. Theory Related Fields,103, 515–528 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  12. R. Cuppens,Decomposition of Multivariate Probability, Academic Press, New York-San Francisco-London (1975).

    Google Scholar 

  13. P. Deheuvels and D. Pfeifer, A semigroup approach to Poisson approximation,Ann. Probab.,14, 663–676 (1986).

    MATH  MathSciNet  Google Scholar 

  14. J. Dhaene and N. De Pril, On a class of approximative computation methods in the individual risk model,Insurance: Math. and Economics,14, 181–196 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  15. P. Franken, Approximation der Verteilungen von Summen unabhängiger nichtnegativen ganzzahlinger Zufalgrösen durch Poissonsche Verteilungen,Math. Nachr.,27, 303–340 (1964).

    MATH  MathSciNet  Google Scholar 

  16. C. Hipp, Improved approximations for the aggregate clains distribution in the individual model.ASTIN Bull.,16, 89–100 (1987).

    Article  Google Scholar 

  17. P. Kornya, Distribution of aggregate claims in the Individual Risk Theory model,Society of Actuaries: Transactions,35, 823–858 (1983).

    Google Scholar 

  18. A. Kovats, Bergström type asymptotic expansions for sums of integer-valued random variables and vectors [in Russian], Ph.D. Thesis, Vilnius (1983).

  19. S. Kuon, A. Reich and L. Reinmers, Panjer vs. Kornya vs. De Pril: a comparison from a practical point of view,ASTIN Bull.,17, 183–191 (1987).

    Article  Google Scholar 

  20. Yu. Kruopis, Approximations for distributions of sums of lattice random variables I,Lith. Math. J.,26, 234–244 (1986).

    Article  MATH  Google Scholar 

  21. S. V. Nagaev and V. I. Chebotarev, On asymptotic expansions of Bergström type in Hilbert space,Trudy Inst. Mat. (Novosibirsk),13, 66–77 (1989).

    MATH  MathSciNet  Google Scholar 

  22. E. L. Presman, Approximation of binomial distributions by infinitely divisible ones,Theory Probab. Appl.,28, 393–403 (1983).

    Article  MathSciNet  Google Scholar 

  23. 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).

    Article  MathSciNet  Google Scholar 

  24. 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).

    Article  MATH  Google Scholar 

  25. 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, 657–669 (1984).

    Article  Google Scholar 

  26. A. Yu. Zaitsev, On a multidimensional generalization of the triangular functions method,Zap. Nauchn. Sem. LOM1,158, 81–104 (1987).

    Google Scholar 

  27. A. Yu. Zaitsev, Estimates of closeness of successive convolutions of multidimensional symmetric distributions,Probab. Theory Related Fields,79, 175–200 (1988).

    Article  MATH  MathSciNet  Google Scholar 

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Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 37, No. 4, pp. 426–447, October–December, 1997.

Translated by V. Čekanavičius

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Čekanavičius, V. Asymptotic expansions for compound Poisson measures. Lith Math J 37, 320–336 (1997). https://doi.org/10.1007/BF02465574

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  • DOI: https://doi.org/10.1007/BF02465574

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