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Randomized divisible statistics in a scheme of independent allocation of particles on cells. (Russian) Zbl 0711.60011
n particles are distributed independently of each other into infinitely many cells numbered by 1,2,.... A particle hits the m th cell with probability \(p_ m\geq 0\), \(\sum^{\infty}_{m=1}p_ m=1\). Let \(\eta_ m=\eta_ m(n)\) denote the number of particles thrown into the m th cell, and let \(\{f_ m^{(n)}(y)\), \(m=1,2,...\}\) be a sequence of random functions of the non-negative and integer argument y. Randomized divisible statistics R(\(\eta\)) are defined by \[ R(\eta)=\sum^{\infty}_{m=1}f_ m^{(n)}(y), \] assuming that this series converges with probability 1. The author considers various applications of his previous results [see ibid. 1, No.4, 46-62 (1989)] concerning the asymptotic behaviour of R(\(\eta\)) as \(n\to \infty\).
Reviewer: L.Mutafchiev

60C05 Combinatorial probability
62F05 Asymptotic properties of parametric tests
60F05 Central limit and other weak theorems