What is Kurtosis? An Influence Function Approach

Abstract The standard fourth moment coefficient of kurtosis is introduced in many textbooks including those at the elementary level, yet the measure is not well understood. It is often regarded as a measure of the tail heaviness of a distribution, relative to that of the normal distribution. Other authors assert that kurtosis measures peakedness near the center of the distribution. In this article, Hampel's influence function is used to assess the relative importance of tail heaviness and peakedness for the standard kurtosis measure and some related measures. Some notions of comparative kurtosis are also discussed.