KURTOSIS AND SPREAD

An increase in kurtosis is achieved through the location‐ and scale‐free movement of probability mass from the “shoulders” of a distribution into its centre and tails. We introduce a coherent structure of ordering and measures, requiring no symmetry assumption, that represent different formalizations of this movement. For this purpose spread functions and spread‐spread plots are defined. The orderings impose growth patterns on the spread‐spread plot of the distributions involved, and the weakest involve both a specific scale‐matching technique and placement of “shoulders”. The role of existing kurtosis orderings and measures in this general context is identified and examples discussed throughout. Copyright © 1990 Statistical Society of Canada