SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

Mathematica > Data Manipulation > Statistics > Descriptive Statistics >

Mathematica > Mathematics and Algorithms > Statistics > Descriptive Statistics >

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[{{x₁, y₁, ...}, {x₂, y₂, ...}, ...}] gives {Kurtosis[{x₁, x₂, ...}], Kurtosis[{y₁, y₂, ...}], ...}.

Kurtosis for a list of values:

Kurtosis for a symbolic distribution:

Kurtosis for a list of values:

Kurtosis for a symbolic distribution:

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 a distribution can be computed from ExpectedValue and Variance:

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: