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1987•Communications in Statistics - Simulation and ComputationRequires access

Characterizing parameters of multivariate elliptical distributions*

Maia Berkane, Peter M. Bentler

Open publisher page 13 citations

Abstract

This paper defines new parameters characterizing multivariate elliptical distributions. Mardia's coefficient of multivariate kurtosis is shown to be essentially one of these parameters. A simple relation is established between centered multivariate product moments and second moments of the variables. The general results are verified on the contaminated normal distribution as an example.

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What this paper is about

This paper defines new parameters characterizing multivariate elliptical distributions. Mardia's coefficient of multivariate kurtosis is shown to be essentially one of these parameters. A simple relation is established between centered multivariate product moments and second moments of the variables. The general results are verified on the contaminated normal distribution as an example.

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OpenAlex reports 13 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper defines new parameters characterizing multivariate elliptical distributions. Mardia's coefficient of multivariate kurtosis is shown to be essentially one of these parameters. A simple relation is established between centered multivariate product moments and second moments of the variables. The general results are verified on the contaminated normal distribution as an example.

Key concepts: Multivariate statistics, Kurtosis, Elliptical distribution, Mathematics, Multivariate analysis, Multivariate stable distribution, Matrix t-distribution, Simple (philosophy)

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