Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.


The kurtosis (or excess)  measures the relative flatness of a distribution (as compared to the normal distribution, which shows a kurtosis of zero). A positive kurtosis indicates a tapering distribution (also called leptokurtic distribution), whereas a negative kurtosis indicates a flat distribution (platykurtic distribution). Distributions resembling a normal distribution are sometimes called mesocurtic distributions.

The kurtosis is defined by the following formula:(1)

This equation of the kurtosis is valid for a sample and is a biased estimator of the kurtosis of the population. In order to estimate the kurtosis of the population you have to use the following formula:

Below you find two examples of distributions with different kurtosis.

(1) Note that the kurtosis is sometimes defined by another formula, omitting the term "-3" in the formula above. In this case a normal distribution would yield a kurtosis of 3.