Important: The stats package has been deprecated. Use the superseding package Statistics instead.

The function kurtosis of the subpackage stats[describe, ...] computes the moment coefficient of kurtosis of the given data. It is defined to be the fourth moment about the mean, divided by the fourth power of the standard deviation.

The kurtosis measures the degree to which a distribution is flat or peaked. For the normal distribution (mesokurtic), the kurtosis is 3. If the distribution has a flatter top (platykurtic), the kurtosis is less than 3. If the distribution has a high peak (leptokurtic), the kurtosis is greater than 3.

Classes are assumed to be represented by the class mark, for example 10..12 has the value 11. Missing data are ignored.

The definition of standard deviation varies according to whether it is computed for the whole population, or only for a sample. It follows then that the kurtosis also depends on this factor, which is controlled by the parameter Nconstraint. For more information on this, refer to describe[standarddeviation].

There are other possibilities for the definition of the kurtosis, as can be seen in various books on statistics.

The command with(stats[describe],kurtosis) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{stats}\right)\:$

$\mathrm{describe}\left[\mathrm{kurtosis}\right]\left(\left[0\,1.0\,\mathrm{Weight}\left(2\,2\right)\,\mathrm{Weight}\left(3\,2\right)\,\mathrm{Weight}\left(4\,2\right)\,5\,6\right]\right)$

$2.199999998$

$\mathrm{describe}\left[\mathrm{kurtosis}\right]\left(\left[0\,1.0\,\mathrm{Weight}\left(2\,2\right)\,\mathrm{Weight}\left(3\,6\right)\,\mathrm{Weight}\left(4\,2\right)\,5\,6\right]\right)$

$3.080000003$

$\mathrm{describe}\left[\mathrm{kurtosis}\right]\left(\left[0\,1.0\,\mathrm{Weight}\left(2\,2\right)\,\mathrm{Weight}\left(3\,20\right)\,\mathrm{Weight}\left(4\,2\right)\,5\,6\right]\right)$

$6.159999998$