Kurtosis and Skewness

Functions > Statistics > Descriptive Statistics > Kurtosis and Skewness

• kurt(A, B, C, ...)—Returns the kurtosis of the elements A, B, C, .... The kurtosis is defined as follows:

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The kurtosis of a set of values indicates how flat or peaked the distribution is when compared to the normal distribution:

Value	Distribution Shape
kurt = 0	Normal distribution
kurt > 0	Relatively peaked distribution
kurt < 0	Relatively flat distribution

• skew(A, B, C, ...)—Returns the skewness of the elements A, B, C, .... The skewness is defined as follows:

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                        <id xml:space="preserve">mean</id>
                        <id xml:space="preserve">M</id>
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                      <id xml:space="preserve">Stdev</id>
                      <id xml:space="preserve">M</id>
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                <real>3</real>
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            <lowerBound>
              <real>0</real>
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                <id xml:space="preserve">n</id>
                <real>1</real>
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          <real>0</real>
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The skewness of a set of values measures the asymmetry about the mean:

Value	Distribution Shape
skew = 0	The distribution is symmetric about its mean, as is the case for the normal distribution.
skew > 0	The distribution "tail" extends towards positive values.
skew < 0	The distribution "tail" extends towards negative values.

Arguments

• A, B, C, ... are scalars or arrays. There must be at least four elements in the arguments for kurt, and at least three for skew.

• M is an array created from the function arguments A, B, C, .... The standard deviation of M must not equal zero.