Multivariate statistical simulation
Multivariate statistical simulation
Elliptically contoured models in statistics
Elliptically contoured models in statistics
Color-image watermarking using multivariate power- exponential distribution
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Statistical inference for the ε-entropy and the quadratic Rényi entropy
Journal of Multivariate Analysis
Notes: A multivariate ultrastructural errors-in-variables model with equation error
Journal of Multivariate Analysis
Multivariate measures of skewness for the skew-normal distribution
Journal of Multivariate Analysis
A necessary test of fit of specific elliptical distributions based on an estimator of Song's measure
Journal of Multivariate Analysis
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The main objective of this paper is the calculation and the comparative study of two general measures of multivariate kurtosis, namely Mardia's measure @b"2","p and Song's measure S(f). In this context, general formulas for the said measures are derived for the broad family of the elliptically contoured symmetric distributions and also for specific members of this family, like the multivariate t-distribution, the multivariate Pearson type II, the multivariate Pearson type VII, the multivariate symmetric Kotz type distribution and the uniform distribution in the unit sphere. Analytic expressions for computing Shannon and Renyi entropies are obtained under the elliptic family. The behaviour of Mardia's and Song's measures, their similarities and differences, possible interpretations and uses in practice are investigated by comparing them in specific members of the elliptic family of multivariate distributions. An empirical estimator of Song's measure is moreover proposed and its asymptotic distribution is investigated under the elliptic family of multivariate distributions.