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Counting and enumerating frequency tables with given margins

digital Counting and enumerating frequency tables with given margins
Article
journal STATISTICA & APPLICAZIONI
issue STATISTICA & APPLICAZIONI - 2003 - 2
title Counting and enumerating frequency tables with given margins
author
publisher Vita e Pensiero
format Article | Pdf
online since 01-07-2016
issn 18246672 (print)
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The problem of finding the number of rectangular tables of non-negative integers with given row and column sums occurs in many interesting contexts, mainly in combinatorial problems (counting magic squares, enumerating permutation by descents, etc.) and in statistical applications (studying contingency tables with given margins, testing for independence, etc.). In the present paper a new recursive argument is presented to produce a general expression for the number of m×n tables with given margins. The result has the same expressive force of the one presented by Gail and Mantel (1977), but, remarkably, the counting approach suggests, quite naturally, also a recursive algorithm to explicitly generate the entire class of tables.
This work is a necessary step for studying a new measure of association, based on the relative position that a given table assumes in its class, endowed by an association ordering.

Keywords: Contingency tables, frequency tables, enumeration of contingency tables with given margins, counting contingency tables with given margins.

Author biography

Francesca Greselin, Dipartimento di Metodi Quantitativi per le Scienze Economiche e Aziendali, Università degli Studi di Milano Bicocca, Piazza dell’Ateneo Nuovo 1, Milano, I-20126, Italy (e-mail: francesca.greselin@unimib.it).

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