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


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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.

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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.

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

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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].

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

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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.
>


This data has a flatter distribution than the normal distribution.
>


 (1) 
This data has about the same flatness as the normal distribution.
>


 (2) 
This data is more sharply peaked that then normal distribution.
>


 (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.


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