THE RELATIONSHIPS BETWEEN SKEWNESS AND KURTOSIS

Theoretical considerations of kurtosis, whether of partial orderings of distributions with respect to kurtosis or of measures of kurtosis, have tended to focus only on symmetric distributions. With reference to historical points and recent work on skewness and kurtosis, this paper defines anti-skewness and uses it as a tool to discuss the concept of kurtosis in asymmetric univariate distributions. The discussion indicates that while kurtosis is best considered as a property of symmetrised versions of distributions, symmetrisation does not simply remove skewness. Skewness, anti-skewness and kurtosis are all inter-related aspects of shape. The Tukey g and h family and the Johnson Su family are considered as examples.