Moments of separable statistics in a generalized distribution scheme
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\(\to \infty\).
scientific article; zbMATH DE number 3992619
scientific article