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

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  • Steyn, H. S.

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.

Suggested Citation

  • Steyn, H. S., 1993. "On the Problem of More Than One Kurtosis Parameter in Multivariate Analysis," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 1-22, January.
    • Handle: RePEc:eee:jmvana:v:44:y:1993:i:1:p:1-22
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    1. repec:jss:jstsof:19:i03 is not listed on IDEAS
    2. Ke-Hai Yuan & Peter Bentler, 2004. "On the asymptotic distributions of two statistics for two-level covariance structure models within the class of elliptical distributions," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 437-457, September.
    3. Headrick, Todd C. & Sheng, Yanyan & Hodis, Flaviu-Adrian, 2007. "Numerical Computing and Graphics for the Power Method Transformation Using Mathematica," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i03).
    4. Mohan D. Pant & Todd C. Headrick, 2017. "Simulating Uniform- and Triangular- Based Double Power Method Distributions," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(1), pages 1-1.

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