ABSTRACT
Informally, a distribution which is ‘more kurtotic’ has heavier tails, is more peaked at its center (e.g. the mode or median), and has lighter shoulders (e.g. lighter density around the quartiles). “An increase in kurtosis is achieved through the location- and scale-free movement of probability mass from the ‘shoulders’ of a distribution into its center and tails”. This chapter considers three kurtosis orderings based on: moment kurtosis, centile kurtosis, and Balanda-MacGillivray kurtosis. These kurtosis orderings are defined and used to compare the kurtosis of different distributions, initially comparing with the normal distribution to see if it is leptokurtic or platykurtic. In order to distinguish a loosely-defined kurtosis parameter from the explicitly defined kurtosis, a ‘true’ kurtosis parameter is defined as a parameter which changes monotonically with one of the moment, centile, or Balanda-MacGillivray kurtosis orderings.
