Counting and enumerating frequency tables with given margins

digital

Article

Magazine

STATISTICA & APPLICAZIONI

Section

Open Access

Title

Counting and enumerating frequency tables with given margins

Author

Francesca Greselin

Publisher

Vita e Pensiero

Format

Article |

Pdf

Online from

09-2017

Issn

1824-6672 (print) | 2283-6659 (digital)

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Description Readers' comments

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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