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Convergence of the Distributions Generated by Linear Plans of Multidimensional Pólya Random Walks to the α-Generalized Poisson Distribution

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For linear plans of the first entry ΠG of (N + 1)-dimensional Pólya random walks with the stopping boundary \( G:\sum \limits_{m=0}^N{a}_m{x}_m=n \) the closedness domain and asymptotic estimates of some numerical characteristics are found. The authors describe the scenarios for convergence of the distributions generated by linear plans of these walks in the domain of “rare events” to the N-dimensional α- generalized Poisson distribution for a rather wide range \( n\alpha \in \left(-\frac{1}{2},1\right) \) of the parameters of Pólya walks. Special cases of this result for linear plans of polynomial and multidimensional hypergeometric walks are considered.

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Authors and Affiliations

  1. Perm National Research Polytechnic University, Perm, Russia

    E.G. Tsylova

  2. Kamensk-Uralskiy Tehnikum of Trade and Service, Kamensk-Uralskiy, Russia

    E. Y. Ekgauz

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  1. E.G. Tsylova
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  2. E. Y. Ekgauz
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Correspondence to E.G. Tsylova.

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Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 23, pp. 61–76, 2011

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Tsylova, E., Ekgauz, E.Y. Convergence of the Distributions Generated by Linear Plans of Multidimensional Pólya Random Walks to the α-Generalized Poisson Distribution. J Math Sci 267, 81–91 (2022). https://doi.org/10.1007/s10958-022-06110-5

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