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Home Univariate Data Moments of a Distribution Kurtosis
See also: skewness, moments of a distribution 

Kurtosis

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.


Home Univariate Data Moments of a Distribution Kurtosis