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On the theory of elliptically contoured distributions

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  • Cambanis, Stamatis
  • Huang, Steel
  • Simons, Gordon
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    Abstract

    The theory of elliptically contoured distributions is presented in an unrestricted setting, with no moment restrictions or assumptions of absolute continuity. These distributions are defined parametrically through their characteristic functions and then studied primarily through the use of stochastic representations which naturally follow from the work of Schoenberg [5] on spherically symmetric distributions. It is shown that the conditional distributions of elliptically contoured distributions are elliptically contoured, and the conditional distributions are precisely identified. In addition, a number of the properties of normal distributions (which constitute a type of elliptically contoured distributions) are shown, in fact, to characterize normality.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 11 (1981)
    Issue (Month): 3 (September)
    Pages: 368-385

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    Handle: RePEc:eee:jmvana:v:11:y:1981:i:3:p:368-385

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    Related research

    Keywords: Elliptically contoured multivariate spherically symmetric characteristic function Laplace transform conditional distribution characterizations of normality;

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