Approximation by Poisson law

Aldona Aleškevičienė; Vytautas Statulevičius

Discussiones Mathematicae Probability and Statistics (2005)

  • Volume: 25, Issue: 2, page 161-179
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Aldona Aleškevičienė, and Vytautas Statulevičius. "Approximation by Poisson law." Discussiones Mathematicae Probability and Statistics 25.2 (2005): 161-179. <http://eudml.org/doc/287608>.

@article{AldonaAleškevičienė2005,
abstract = {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.},
author = {Aldona Aleškevičienė, Vytautas Statulevičius},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Poisson distribution; compound Poisson distribution; asymptotic expansions; large deviations; cumulants},
language = {eng},
number = {2},
pages = {161-179},
title = {Approximation by Poisson law},
url = {http://eudml.org/doc/287608},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Aldona Aleškevičienė
AU - Vytautas Statulevičius
TI - Approximation by Poisson law
JO - Discussiones Mathematicae Probability and Statistics
PY - 2005
VL - 25
IS - 2
SP - 161
EP - 179
AB - 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.
LA - eng
KW - Poisson distribution; compound Poisson distribution; asymptotic expansions; large deviations; cumulants
UR - http://eudml.org/doc/287608
ER -

References

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  1. [1] A. Aleskeviciene, Probabilities of large deviations in approximation by the Poisson law, Lithuanian Math. J. 28 (1988), 3-13. 
  2. [2] A. Aleskeviciene and V. Statulevicius, Asymptotic expansions in the approximation by the Poisson law, Lithuanian Math. J. 34 (1996), 1-21. 
  3. [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. [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. 
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  6. [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. [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. [8] A.D. Barbour, Asymptotic expansions in the Poisson limit theorem, Ann. Probab. 15 (1987), 748-766. Zbl0622.60049
  9. [9] H.Y. Chen Louis and R.P. Choi, Some asymptotic and large deviations results in Poisson approximation, Ann. Probab. 20 (1992), 1867-1876. Zbl0764.60026
  10. [10] P. Deheuvels, Large deviations by Poisson approximations, J. Statist. Planning Inference 32 (1992), 75-88. Zbl0758.60023
  11. [11] P. Franken, Approximation der Verteilungen von Summen unabhangiger nichtnegativer ganzahliger Zuffallsgrossen duren Poissonsche Verteilungen, Mathematische Nachrichten 27 (1964), 303-340. Zbl0192.25204
  12. [12] J. Macys, Stability of decomposition into components of a discontinuous distribution function in uniform metric, Lithuanian Mathem. J. 35 (1995), 105-117. Zbl0847.60014
  13. [13] S.Ya. Shorgin, Approximation of generalized binoaminal distribution, Probab. Theory Appl. 22 (1977), 867-871. 
  14. [14] L. LeCam, An approximation theorem for the Poisson binomial distribution, Pacific J. Math. 10 (1960), 1181-1197. Zbl0118.33601
  15. [15] R.J. Serfling, A general Poisson approximation theorem, Ann. Probab. 3 (1975), 726-731. Zbl0321.60018
  16. [16] B.V. Gnedenko and A.N. Kolmogorov, Limit distribution for sums of independent random variables, Addison-Wesley, Reading 1954. Zbl0056.36001

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