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Approximation for expectations of unbounded functions of dependent integer-valued random variables

Part of: Limit theorems Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Pavel S. Ruzankin
Pavel S. Ruzankin*
Affiliation:
Sobolev Institute of Mathematics
*
∗Postal address: Novosibirsk State University, Sobolev Institute of Mathematics, pr. Ak. Koptyuga 4, Novosibirsk, 630090, Russia. Email address: ruzankin@math.nsc.ru
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Abstract

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Expectations of unbounded functions of dependent nonnegative integer-valued random variables are approximated by the expectations of the functions of independent copies of these random variables. The Lindeberg method is used.

Keywords

Unbounded functionreliability systemPoisson approximationLindeberg's method

MSC classification

Secondary: 60F05: Central limit and other weak theorems 60E07: Infinitely divisible distributions; stable distributions
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 2 , June 2010 , pp. 594 - 600
Copyright
Copyright © Applied Probability Trust 2010 

Footnotes

Research partially supported by th RFBR under 09-01-12131 and 09-01-00738.

References

Barbour, A. D. (1987). Asymptotic expansions in the Poisson limit theorem. Ann. Prob. 15, 748–766.CrossRefGoogle Scholar
Barbour, A. D. and Chryssaphinou, O. (2001). Compound Poisson approximation: a user's guide. Ann. Appl. Prob. 11, 964–1002.Google Scholar
Barbour, A. D. and Hall, P. (1984). On the rate of Poisson convergence. Math. Proc. Camb. Phil. Soc. 95, 473–480.Google Scholar
Barbour, A. D., Novak, S. Y. and Xia, A. (2002). Compound Poisson approximation for the distribution of extremes. Adv. Appl. Prob. 34, 223–240.Google Scholar
Borisov, I. S. and Ruzankin, P. S. (2002). Poisson approximation for expectations of unbounded functions of independent random variables. Ann. Prob. 30, 1657–1680.CrossRefGoogle Scholar