Abstract:
It is shown that the results obtained earlier for the rate of approximation of convolutions of probability distributions by accompanying infinitely divisible laws may be interpreted as estimates of the rate of approximation of the sample by a Poisson point process. The most interesting results are obtained for a scheme of rare events.
Citation:
A. Yu. Zaitsev, “On approximation of the sample by a Poisson point process”, Probability and statistics. Part 6, Zap. Nauchn. Sem. POMI, 298, POMI, St. Petersburg, 2003, 111–125; J. Math. Sci. (N. Y.), 128:1 (2005), 2556–2563
\Bibitem{Zai03}
\by A.~Yu.~Zaitsev
\paper On approximation of the sample by a~Poisson point process
\inbook Probability and statistics. Part~6
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 298
\pages 111--125
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1156}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2038866}
\zmath{https://zbmath.org/?q=an:1086.60029}
\elib{https://elibrary.ru/item.asp?id=14563167}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 128
\issue 1
\pages 2556--2563
\crossref{https://doi.org/10.1007/s10958-005-0202-3}
Linking options:
https://www.mathnet.ru/eng/znsl1156
https://www.mathnet.ru/eng/znsl/v298/p111
This publication is cited in the following 12 articles:
F. Götze, A. Yu. Zaitsev, “Convergence to Infinite-Dimensional Compound Poisson Distributions on Convex Polyhedra”, J Math Sci, 273:5 (2023), 732
F. Götze, A. Yu. Zaitsev, “On alternative approximating distributions in the multivariate version of Kolmogorov's second uniform limit theorem”, Theory Probab. Appl., 67:1 (2022), 1–16
V. Čekanavičius, S. Y. Novak, “Compound Poisson approximation”, Probab. Surveys, 19:none (2022)
F. Gettse, A. Yu. Zaitsev, “Skhodimost k beskonechnomernym obobschennym raspredeleniyam Puassona na vypuklykh mnogogrannikakh”, Veroyatnost i statistika. 30, Zap. nauchn. sem. POMI, 501, POMI, SPb., 2021, 118–125
S. Y. Novak, “Poisson approximation”, Probab. Surveys, 16:none (2019)
F. Gettse, A. Yu. Zaitsev, “Otsenki blizosti svertok veroyatnostnykh raspredelenii na vypuklykh mnogogrannikakh”, Veroyatnost i statistika. 27, Zap. nauchn. sem. POMI, 474, POMI, SPb., 2018, 108–117
Lifshits M.A. Nikitin Ya.Yu. Petrov V.V. Zaitsev A.Yu. Zinger A.A., “Toward the History of the Saint Petersburg School of Probability and Statistics. i. Limit Theorems For Sums of Independent Random Variables”, Vestn. St Petersb. Univ.-Math., 51:2 (2018), 144–163
F. Götze, Yu. S. Eliseeva, A. Yu. Zaitsev, “Arak inequalities for concentration functions and the Littlewood–Offord problem”, Theory Probab. Appl., 62:2 (2018), 196–215
F. Gettse, A. Yu. Zaitsev, “Redkie sobytiya i puassonovskie tochechnye protsessy”, Veroyatnost i statistika. 26, Zap. nauchn. sem. POMI, 466, POMI, SPb., 2017, 109–119
Kruopis J., Cekanavicius V., “Compound Poisson Approximations For Symmetric Vectors”, J. Multivar. Anal., 123 (2014), 30–42
Pavel Samusenko, Nonparametric criteria for sparse contingency tables, 2012
Citation in format AMSBIB
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