Moments of separable statistics in a generalized distribution scheme
type: Item
instance of: scholarly article
title: Moments of separable statistics in a generalized distribution scheme
zbMATH Open document ID: 0613.62010
DOI: 10.1007/BF01159901
author: G. I. Ivchenko
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: Let \(\eta (n)=(\eta_ 1(n),...,\eta_ N(n))\) denote a random vector with non-negative integer-valued coordinates depending on a parameter n and let \[ P\{\eta_ j(n)=k_ j,\quad j=1,...,N\}=P\{\xi_ j=k_ j,\quad j=1,...,N| \quad \xi_ 1+...+\xi_ N=n\}, \] where \(\xi_ j\) are independent non-negative integer-valued random variables such that \(P\{\xi_ 1+...+\xi_ N=n\}>0\). The author considers the random variables \(L_ N(\eta (n))=\sum^{N}_{m=1}f_{N,m}(\eta_ m(n))\), where \(f_{N,m}\) are arbitrary measurable functions. He proposes a method for deriving asymptotic formulas of the moments of \(L_ N(\eta (n))\) as n,N\(\to \infty\).
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 3992619
zbMATH Keywords: separable statistics
zbMATH Keywords: generalized distribution scheme
zbMATH Keywords: asymptotic formulas
zbMATH Keywords: moments
reviewed by: Ljuben Mutafchiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3992619