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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1067,
author = {Aldona Ale\v skevi\v cien\.e and Vytautas Statulevi\v cius},
title = {Approximation by Poisson law},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {25},
year = {2005},
pages = {161-179},
zbl = {1102.62013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1067}
}
Aldona Aleškevičienė; Vytautas Statulevičius. Approximation by Poisson law. Discussiones Mathematicae Probability and Statistics, Tome 25 (2005) pp. 161-179. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1067/
[000] [1] A. Aleskeviciene, Probabilities of large deviations in approximation by the Poisson law, Lithuanian Math. J. 28 (1988), 3-13.
[001] [2] A. Aleskeviciene and V. Statulevicius, Asymptotic expansions in the approximation by the Poisson law, Lithuanian Math. J. 34 (1996), 1-21.
[002] [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.
[003] [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.
[004] [5] A. Aleskeviciene and V. Statulevicius, Large deviations in the approximation by Poisson law, Probab. Theory Appl. 46 (2001), 625-639.
[005] [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.
[006] [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.
[007] [8] A.D. Barbour, Asymptotic expansions in the Poisson limit theorem, Ann. Probab. 15 (1987), 748-766. | Zbl 0622.60049
[008] [9] H.Y. Chen Louis and R.P. Choi, Some asymptotic and large deviations results in Poisson approximation, Ann. Probab. 20 (1992), 1867-1876. | Zbl 0764.60026
[009] [10] P. Deheuvels, Large deviations by Poisson approximations, J. Statist. Planning Inference 32 (1992), 75-88. | Zbl 0758.60023
[010] [11] P. Franken, Approximation der Verteilungen von Summen unabhangiger nichtnegativer ganzahliger Zuffallsgrossen duren Poissonsche Verteilungen, Mathematische Nachrichten 27 (1964), 303-340. | Zbl 0192.25204
[011] [12] J. Macys, Stability of decomposition into components of a discontinuous distribution function in uniform metric, Lithuanian Mathem. J. 35 (1995), 105-117. | Zbl 0847.60014
[012] [13] S.Ya. Shorgin, Approximation of generalized binoaminal distribution, Probab. Theory Appl. 22 (1977), 867-871.
[013] [14] L. LeCam, An approximation theorem for the Poisson binomial distribution, Pacific J. Math. 10 (1960), 1181-1197. | Zbl 0118.33601
[014] [15] R.J. Serfling, A general Poisson approximation theorem, Ann. Probab. 3 (1975), 726-731. | Zbl 0321.60018
[015] [16] B.V. Gnedenko and A.N. Kolmogorov, Limit distribution for sums of independent random variables, Addison-Wesley, Reading 1954. | Zbl 0056.36001