Kurtosis as Peakedness: The Phoenix from the Ashes
Foundations for Scientific Investing, Eighth Edition, January 2019
12 Pages Posted: 26 Sep 2016 Last revised: 5 Feb 2019
Date Written: January 1, 2019
It has recently been argued that we should no longer associate peakedness with kurtosis (Westfall, 2014). The main part of the argument is based on a decomposition of kurtosis into terms associated with the center or with the tails of a distribution. Simple empirical, simulated, and analytical counter arguments are given to show that this decomposition is incorrect, because it is inconsistent with Pearson’s (1902, 1905) basic thesis. In fact, the level of kurtosis of a distribution is typically strongly influenced by the shape of the center of the distribution. We must, however, be cautious in describing the excess kurtosis of a symmetric distribution as a function of its peakedness relative to a normal distribution with the same variance — because of a mistake by Pearson that has often been overlooked.
Keywords: kurtosis, peakedness, fat tails, Pearson, Westfall
JEL Classification: C46, C58, G12
Suggested Citation: Suggested Citation