Contents
- Index
Kurtosis
The fourth moment of a distribution and the second shape parameter. The kurtosis is a measure of the heavy the tails are. The normal distribution shown below has a kurtosis of 3:
A kurtosis greater than 3 means the tails are heavier than the normal distribution. In order to have more units in the extreme tails also means there must also be more units near the middle of the distribution. Such distributions appear to have a very high peak in the middle with wide plateaus for tail. An example is the logistic distribution with a kurtosis of 4.2 shown below:
A kurtosis less than 3 means the tails are lighter than the normal distribution like the Uniform distribution with a kurtosis of 1.8 shown below:
A kurtosis value of 4 and above or 2 and below represents a sizable departure from normality. The formula used for estimating the kurtosis from a set of data is:
where n is the sample size, 
represents the data points, 
is the average and S is the standard deviation.
The excess kurtosis = kurtosis - 3. This results in the normal distribution having an excess kurtosis of zero.