References
B. V. Gnedenko and A. N. Kolmogorov,Limiting Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading, MA (1968).
B. Grigelionis, On an asymptotic decomposition of the remainder term in the case of convergence to the Poisson law,Lith. Math. J. 2, 35–48 (1962).
P. Franken, Approximation der Verteilungen von Summen unabhängiger nichtnegativer ganzzahliger Zufallsgrosser durch Poissonsche Verteilungen,Mathematische Nachrichten,27, 303–340 (1964).
S. Ya. Shorgin, Approximation of generalized binomial distribution,Probab. Appl.,22 867–871 (1977).
J. Milaševičius, On the convergence of Grigelionis-Franken's asymptotic expansions,Appl. Probab. Theory Statistics,3, 87–110 (1980).
A. D. Barbour, Asymptotic expansions in the Poisson limit theorem,Ann. Probab.,15, 748–766 (1987).
A. K. Aleškevičiené and V. A. Statulevčius, Large deviations in approximation by Poisson law, in:Probability Theory and Mathematical Statistics, Proceedings of the Sixth Vilnius Conference, VSP, Utrecht/TEV, Vilnius (1994), pp. 1–14.
I. P. Tsaregradskij, On uniform approximation of the binomial distribution by infinitely divisible laws,Theory Probab. Appl.,3, 470–474 (1958).
V. V. Petrov,Limit Theorems for Sums of Independent Random Variables, [in Russian], Nauka, Moscow (1972).
L. Saulis and V. A. Statulevičius,Limit Theorems for Large Deviations, Kluwer Academic Publishers, Dordrecht (1991).
V. M. Zolotarev,Modern Theory of the Summation of Idependent Random Variables, [in Russian], Nauka, Moscow (1986).
A. K. Aleškevičiené and V. A. Statulevičius, On the inverse formula in the case of the discontinuous limit law,Theory Probab. Appl. (1996) (in press).
J. Mačys, Stability of decomposition into components of a discontinuous distribution function in uniform metric,Lith. Math. J.,35, 105–117 (1995).
J. Kruopis, On exactness the Poisson measure convolution approximations for generalised binomial distribution,Lith. Math. J.,26, 53–69 (1986).
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Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Vytautas Magnus University, Daukanto 28 3000 Kaunas, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 4, pp. 393–414, October–December 1995.
Translated by A. K. Aleškevičiené and V. A. Statulevičius
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Aleškevičiené, A.K., Statulevičius, V.A. Asymptotic expansions in the approximation by the poisson law. Lith Math J 35, 309–327 (1995). https://doi.org/10.1007/BF02335592
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DOI: https://doi.org/10.1007/BF02335592