Kurtosis: A Critical Review

We critically review the development of the concept of kurtosis. We conclude that it is best to define kurtosis vaguely as the location- and scale-free movement of probability mass from the shoulders of a distribution into its center and tails and to recognize that it can be formalized in many ways. These formalizations are best expressed in terms of location- and scale-free partial orderings on distributions and the measures that preserve them. The role of scale-matching techniques and placement of shoulders in the formalizations that have appeared in the literature are emphasized.