Conditions are given for linear functions of skew-normal random vectors to maximize skewness and kurtosis. As a direct implication, several measures of their multivariate skewness and kurtosis are shown to be equivalent. An estimator of the shape parameter with good statistical properties is also considered. These results are strictly related to canonical forms of skew-normal distributions and linear transfor- mations to normality.
Canonical Transformations of Skew-Normal Variates
LOPERFIDO, NICOLA MARIA RINALDO
2010
Abstract
Conditions are given for linear functions of skew-normal random vectors to maximize skewness and kurtosis. As a direct implication, several measures of their multivariate skewness and kurtosis are shown to be equivalent. An estimator of the shape parameter with good statistical properties is also considered. These results are strictly related to canonical forms of skew-normal distributions and linear transfor- mations to normality.File in questo prodotto:
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