Sankhya: The Indian Journal of Statistics

2003, Volume 65, Pt. 1, 179--195

Local Dependence Functions For The Elliptically Symmetric Distributions

By

Samuel Kotz, George Washington University, Washington, D.C., USA and

Saralees Nadarajah, University of South Florida, Tampa, USA

SUMMARY. Bairamov {\it et al.} (2000) introduced a measure of local dependence which is a localized version of the Galton correlation coefficient. In this paper we: 1) provide a motivation for this new measure; 2) derive the exact form of the measure for the class of elliptically symmetric distributions; and, 3) provide an application of the new measure to the theory for ordering of bivariate dependence (this involves defining three new concepts for ordering of bivariate dependence and deriving certain asymptotic expansions). We illustrate the results for five examples of elliptically symmetric distributions.

AMS (1991) subject classification. Primary 62H20.

Key words and phrases. Asymptotic expansions, bivariaten normal, correlation coefficient, elliptically symmetric distributions, local dependence function.

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