Abstract:
Let
Sn=1√nn∑j=1(ξj−Mξj)
be the normalized sum of independent equally distributed lattice random vectors ξ1,ξ2,…,ξn. In this paper, asymptotic expansions of the probability function Pn(A), A being a Borel set, of Sn are considered.
Citation:
A. Bikelis, “Asymptotic expansions of the distribution functions of the sums of independent equally distributed lattice random vectors”, Teor. Veroyatnost. i Primenen., 14:3 (1969), 499–507; Theory Probab. Appl., 14:3 (1969), 481–489
\Bibitem{Bik69}
\by A.~Bikelis
\paper Asymptotic expansions of the distribution functions of the sums of independent equally distributed lattice random vectors
\jour Teor. Veroyatnost. i Primenen.
\yr 1969
\vol 14
\issue 3
\pages 499--507
\mathnet{http://mi.mathnet.ru/tvp1203}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=259988}
\zmath{https://zbmath.org/?q=an:0188.23901}
\transl
\jour Theory Probab. Appl.
\yr 1969
\vol 14
\issue 3
\pages 481--489
\crossref{https://doi.org/10.1137/1114060}
Linking options:
https://www.mathnet.ru/eng/tvp1203
https://www.mathnet.ru/eng/tvp/v14/i3/p499
This publication is cited in the following 7 articles:
Christian Genest, Frédéric Ouimet, “Asymptotic comparison of negative multinomial and multivariate normal experiments”, Statistica Neerlandica, 78:2 (2024), 427
N. G. Gamkrelidze, “Issledovaniya po reshetchatym raspredeleniyam teorii veroyatnostei”, Issledovaniya po reshetchatym raspredeleniyam teorii veroyatnostei, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 218, VINITI RAN, M., 2022, 3–66
Frédéric Ouimet, “On the Le Cam distance between Poisson and Gaussian experiments and the asymptotic properties of Szasz estimators”, Journal of Mathematical Analysis and Applications, 499:1 (2021), 125033
Frédéric Ouimet, “A precise local limit theorem for the multinomial distribution and some applications”, Journal of Statistical Planning and Inference, 215 (2021), 218
Haruhiko Ogasawara, “Asymptotic Cumulants of Functions of Multinomial Sample Proportions with Adjustment for Empty Cells”, Behaviormetrika, 39:2 (2012), 211
N. G. Gamkrelidze, “On a measure of smoothness of the multidimensional distributions of integer-valued random vectors”, Theory Probab. Appl., 30:2 (1986), 427–431
D. R. Jensen, “On approximating the distributions ofFriedman's 75-175-175-1and related statistics”, Metrika, 24:1 (1977), 75
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