 describe(deprecated)/kurtosis - Maple Help

stats[describe]

 kurtosis
 Moment Coefficient of Kurtosis Calling Sequence stats[describe, kurtosis](data) stats[describe, kurtosis[Nconstraints]](data) describe[kurtosis](data) describe[kurtosis[Nconstraints]](data) Parameters

 data - statistical list Nconstraint - (optional, default=0) Number of constraints, 1 for sample, 0 for full population Description

 • 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. Examples

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

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

This data has a flatter distribution than the normal distribution.

 > ${\mathrm{describe}}_{\mathrm{kurtosis}}\left(\left[0,1.0,\mathrm{Weight}\left(2,2\right),\mathrm{Weight}\left(3,2\right),\mathrm{Weight}\left(4,2\right),5,6\right]\right)$
 ${2.199999998}$ (1)

This data has about the same flatness as the normal distribution.

 > ${\mathrm{describe}}_{\mathrm{kurtosis}}\left(\left[0,1.0,\mathrm{Weight}\left(2,2\right),\mathrm{Weight}\left(3,6\right),\mathrm{Weight}\left(4,2\right),5,6\right]\right)$
 ${3.080000003}$ (2)

This data is more sharply peaked that then normal distribution.

 > ${\mathrm{describe}}_{\mathrm{kurtosis}}\left(\left[0,1.0,\mathrm{Weight}\left(2,2\right),\mathrm{Weight}\left(3,20\right),\mathrm{Weight}\left(4,2\right),5,6\right]\right)$
 ${6.159999998}$ (3)

Note that these three examples have a symmetrical distribution. Their skewness is then equal to zero. They are not distinguishable from the normal distribution according to the skewness, but they are according to the kurtosis.