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Some Properties of the Kurtosis of a Random Vector

Summary/Abstract: The paper is a continuation of a discussion of the kurtosis of a random vector. Multivariate kurtosis is defined as the fourth central moment divided by the square of the variance of a random vector. This term is built on the definition of the power of a random vector proposed by J. Tatar. The paper presents selected, essential properties of multivariate kurtosis – among other things the invariance property under a number of affine transformations. Besides that, the relation between kurtosis of the random vector and its skewness is fixed. In view of these properties, the fourth central moment divided by the square of the variance of a random vector may be regarded as a satisfactory measure of multivariate kurtosis.

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