On the Problem of More Than One Kurtosis Parameter in Multivariate Analysis

H. S. Steyn

Journal of Multivariate Analysis, 1993, vol. 44, issue 1, 1-22

Abstract: When a multivariate elliptical distribution is used as the basis in multivariate analysis all fourth-order cumulants are expressed in terms of a single kurtosis parameter. This and other well-known properties place unrealistic restrictions on the distribution of the covariance matrix. In this paper a class of elliptical distributions that can be expanded as a power series is first defined. An effort is then made to introduce meaningful multivariate distributions that are related to these elliptical distributions and that contain more than one kurtosis parameter.

Date: 1993
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