This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Kurtosis

 Kurtosis[list]gives the coefficient of kurtosis for the elements in list. Kurtosis[dist]gives the coefficient of kurtosis for the symbolic distribution dist.
• Kurtosis measures the concentration of data around the peak and in the tails versus the concentration in the flanks.
• A kurtosis larger than 3 indicates a distribution that is more peaked and has heavier tails than a normal distribution with the same variance. A kurtosis smaller than 3 indicates a distribution that is flatter.
• Kurtosis handles both numerical and symbolic data.
Kurtosis for a list of values:
Kurtosis for a symbolic distribution:
Kurtosis for a list of values:
 Out[1]=

Kurtosis for a symbolic distribution:
 Out[1]=
 Scope   (5)
Compute results at machine precision:
Obtain results at any precision:
Kurtosis of a matrix will compute column-wise:
Compute results for a large vector or matrix:
Obtain results for continuous and discrete distributions:
Compute results for a SparseArray:
Kurtosis for data can be computed from CentralMoment:
Kurtosis for a distribution can be computed from CentralMoment:
Normal distributions have Kurtosis value 3:
Approximately normal distributions have Kurtosis values near 3:
Plot the PDF for the distribution:
Plot the PDF for the normal approximation:
The kurtosis coefficient is sometimes shifted by 3 to make the normal value 0:
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