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Mat. Zametki, 2013, Volume 93, Issue 1, Pages 56–62 (Mi mz10135)  

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

A. M. Zubkova, T. A. Tatarenkob

a 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 $\{1,2,…\}$ 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

DOI: https://doi.org/10.4213/mzm10135

Full text: PDF file (442 kB)
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English version:
Mathematical Notes, 2013, 93:1, 69–74

Bibliographic databases:

Document Type: Article
UDC: 519.212.2+519.213.23
Received: 11.03.2012

Citation: A. M. Zubkov, T. A. Tatarenko, “The Equivalence between the Schur Order and the Stochastic Orders Generated by the Scheme of Allocation of Particles into Cells”, Mat. Zametki, 93:1 (2013), 56–62; Math. Notes, 93:1 (2013), 69–74

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