The Equivalence between the Schur Order and the Stochastic Orders Generated by the Scheme of Allocation of Particles into Cells

A. M. Zubkov^a, T. A. Tatarenko<sup>b

a</sup> Steklov Mathematical Institute of the Russian Academy of Sciences
^b M. V. Lomonosov Moscow State University

Abstract: In 1982, it was proved that the Schur partial-order relation on the set of distributions on $\{1,2,\dots\}$ is equivalent to the order relation generated the number of nonempty cell distributions by the scheme of independent allocation of particles into cells. Here it is shown that the same partial-order relation is generated by distributions of numbers of cells occupied by at least $r$ particles for any $r\ge 2$.

Keywords: allocation of particles into cells, Schur partial-order relation, stochastic order, multinomial distribution.

UDC: 519.212.2+519.213.23

Received: 11.03.2012

DOI: 10.4213/mzm10135

 English version: Mathematical Notes, 2013, 93:1, 69–74

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