Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 3, 474--486

An Axiomatic Characterization of the Measures of Similarity

By

Carlo Bertoluzza, University of Pavia, Italy
Mario Di Bacco, University of Bologna, Italy
Viviana Doldi, University of Pavia, Italy

SUMMARY. Perhaps the most important task of Descriptive Statistics is the comparison of frequency distributions (f.d.s.), i.e. the evaluation of their similarity or dissimilarity. Many indices of similarity (or dissimilarity) have been proposed in the literature. In this paper, we describe the notion of similarity by means of a system of axioms. The numerical representation of this system provides a class of indices of similarity which includes most of those proposed in the literature. Finally, since the fit of a model of an empirical f.d. can be understood as ``asymmetric" similarity, the class of indices described here also includes indices of fit.

AMS (1991) subject classification}. 62A10.

Key words and phrases. Frequency distributions, measures of similarity, indices of similarity.

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