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2005 | 25 | 2 | 161-179
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Approximation by Poisson law

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present here the results of the investigation on approximation by the Poisson law of distributions of sums of random variables in the scheme of series. We give the results pertaining to the behaviour of large deviation probabilities and asymptotic expansions, to the method of cumulants, with the aid of which our results have been obtained.
Kategorie tematyczne
Rocznik
Tom
25
Numer
2
Strony
161-179
Opis fizyczny
Daty
wydano
2005
otrzymano
2004-03-15
poprawiono
2005-05-16
Twórcy
  • Institute of Mathematics and Informatics, Akademijos 4, Vilnius 2600, Lithuania
  • Institute of Mathematics and Informatics, Akademijos 4, Vilnius 2600, Lithuania
Bibliografia
  • [1] A. Aleskeviciene, Probabilities of large deviations in approximation by the Poisson law, Lithuanian Math. J. 28 (1988), 3-13.
  • [2] A. Aleskeviciene and V. Statulevicius, Asymptotic expansions in the approximation by the Poisson law, Lithuanian Math. J. 34 (1996), 1-21.
  • [3] A. Aleskeviciene and V. Statulevicius, Large deviations in approximation by Poisson law, Probability Theory and Mathematical Statistics. Proceedings of the Sixth Vilnius Conference, VSP, Utrecht/TEV, Vilnius 1994, 1-18.
  • [4] A. Aleskeviciene and V. Statulevicius, Large deviations in power zones in the approximation by the Poisson law, Uspekhi Mathem. Nauk 50 (1995), 63-82.
  • [5] A. Aleskeviciene and V. Statulevicius, Large deviations in the approximation by Poisson law, Probab. Theory Appl. 46 (2001), 625-639.
  • [6] A. Aleskeviciene and V. Statulevicius, Theorems of large deviations in the approximation by the compound Poisson distribution, Acta Applicandae Mathematicae 78 (2003), 21-34.
  • [7] A. Aleskeviciene and V. Statulevicius, On the inverse formula in the case of the discontinuous limit law, Probab. Theory Appl. 42 (1) (1997), 3-20.
  • [8] A.D. Barbour, Asymptotic expansions in the Poisson limit theorem, Ann. Probab. 15 (1987), 748-766.
  • [9] H.Y. Chen Louis and R.P. Choi, Some asymptotic and large deviations results in Poisson approximation, Ann. Probab. 20 (1992), 1867-1876.
  • [10] P. Deheuvels, Large deviations by Poisson approximations, J. Statist. Planning Inference 32 (1992), 75-88.
  • [11] P. Franken, Approximation der Verteilungen von Summen unabhangiger nichtnegativer ganzahliger Zuffallsgrossen duren Poissonsche Verteilungen, Mathematische Nachrichten 27 (1964), 303-340.
  • [12] J. Macys, Stability of decomposition into components of a discontinuous distribution function in uniform metric, Lithuanian Mathem. J. 35 (1995), 105-117.
  • [13] S.Ya. Shorgin, Approximation of generalized binoaminal distribution, Probab. Theory Appl. 22 (1977), 867-871.
  • [14] L. LeCam, An approximation theorem for the Poisson binomial distribution, Pacific J. Math. 10 (1960), 1181-1197.
  • [15] R.J. Serfling, A general Poisson approximation theorem, Ann. Probab. 3 (1975), 726-731.
  • [16] B.V. Gnedenko and A.N. Kolmogorov, Limit distribution for sums of independent random variables, Addison-Wesley, Reading 1954.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1067
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