Derived from the Greek word kurtos (hump), kurtosis refers to the greater or lesser hump of a curve near its maximum, and hence to the greater or lesser length of the tails. Kurtosis is of particular interest in a unimodal frequency distribution, whose curve is bell-shaped. To evaluate this aspect of the shape of a curve, it is compared to a normal curve (also called mesokurtic distribution, which would be the extreme case) having the same overall frequency. It can tell us whether the data is heavy-tailed or light-tailed, relative to a normal distribution. Data with high kurtosis tends to have heavy tails, or outliers; data with low kurtosis tends to have light tails, or lack of outliers. The curve is named:

• leptokurtic if, with respect to the normal curve, there is an excess frequency in the central classes, a lower frequency in intermediate classes, and a higher frequency in the extreme classes. It is therefore a higher distribution at the center and lower at the sides.
• platykurtic if, compared with the normal curve, it has a lower frequency in the central and extreme classes, with a frequency greater than the intermediate ones; it is therefore a lower distribution at the center and higher at the sides.

In the following figure, types of kurtosis in comparison with normal distribution are shown, to highlight the differences:

To measure the kurtosis of a bell-shaped unimodal curve, Pearson's kurtosis index is particularly useful; it shows us how outlier-prone a distribution is. This index is equal to three for normal distribution. Distributions that are more outlier-prone than normal distribution have kurtosis greater than three (leptokurtic distribution); distributions that are less outlier-prone have kurtosis less than three (platykurtic distribution).

In MATLAB, to calculate kurtosis, we can use the kurtosis() function. As an example, we will refer to the same dataset used earlier:

>> Kurt = kurtosis(GlassIdentificationDataSet{:,3:8})
Kurt =
    5.9535    2.5713    4.9848    5.8711   56.3923    9.4990

To assign kurtosis = 0 at the normal distribution, some definitions of kurtosis subtract 3 from the computed value. MATLAB's kurtosis() function does not use this convention.