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Generalized Poisson Distributions as Limits of Sums for Arrays of Dependent Random Vectors

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  • Kobus, M.

Abstract

Arrays of random vectors with values in Rd stationary in rows, are investigated. By the assumptions related to the ones used in the extreme value theory a limit thoerem for sums is proved. Necessary and sufficient conditions for the convergence in distribution of sums to some generalized Poisson distributions in m-dependent and [alpha]-, [rho]-, [phi]-mixing cases are given. As a tool the point processes theory is used.

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  • Kobus, M., 1995. "Generalized Poisson Distributions as Limits of Sums for Arrays of Dependent Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 199-244, February.
    • Handle: RePEc:eee:jmvana:v:52:y:1995:i:2:p:199-244
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    Cited by:

    1. Jakubowski, Adam, 1997. "Minimal conditions in p-stable limit theorems -- II," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 1-20, May.
    2. Raluca M. Balan & Sana Louhichi, 2009. "Convergence of Point Processes with Weakly Dependent Points," Journal of Theoretical Probability, Springer, vol. 22(4), pages 955-982, December.
    3. Tyran-Kaminska, Marta, 2010. "Convergence to Lévy stable processes under some weak dependence conditions," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1629-1650, August.

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