Visualizing Peak and Tails to Introduce Kurtosis

This article proposes a simple method to visualize peak and tails in continuous distributions with finite variance. The excess peak and tails areas in unimodal symmetric and nonsymmetric distributions, and the missing area in U-shaped distributions, are identified by comparing the distribution under consideration with the uniform distribution with equal center and variability. Agreement with kurtosis orderings based on the CDFs, and a strong correlation between the total peak and tails area with quantile kurtosis, were found for the distributions examined. The visualization of tails and peak could be used to introduce the notion of kurtosis in undergraduate statistics courses.