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Kurtosis (excess) of a data sample

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.


stats::kurtosis(x1, x2, …)
stats::kurtosis([x1, x2, …])
stats::kurtosis(s, <c>)


stats::kurtosis(x1, x2, …, xn) returns the kurtosis (the coefficient of excess)


where is the mean of the data xi.

The kurtosis measures whether a distribution is "flat" or "peaked". For normally distributed data, the kurtosis is zero. If the distribution function of the data has a flatter top than the normal distribution, then the kurtosis is negative. The kurtosis is positive, if the distribution function has a high peak compared to the normal distribution.

The column index c is optional, if the data are given by a stats::sample object containing only one non-string column. Cf. Example 3.

External statistical data stored in an ASCII file can be imported into a MuPAD® session via import::readdata. In particular, see Example 1 of the corresponding help page.


Example 1

We calculate the kurtosis of some values:

stats::kurtosis(0, 7, 7, 6, 6, 6, 5, 5, 4, 1)

Alternatively, data may be passed as a list:

stats::kurtosis([2, 2, 4, 6, 8, 10, 10])

Example 2

We create a sample:

stats::sample([[a, 5, 8], [b, 3, 7], [c, d, 0]])
a  5  8
b  3  7
c  d  0

The kurtosis of the second column is:

stats::kurtosis(%, 2)

Example 3

We create a sample consisting of one string column and one non-string column:

stats::sample([["1996", 1242], ["1997", 1353], ["1998", 1142]])
"1996"  1242
"1997"  1353
"1998"  1142

We compute the kurtosis of the second column. In this case this column does not have to be specified, since it is the only non-string column:



x1, x2, …

The statistical data: arithmetical expressions.


A sample of domain type stats::sample.


An integer representing a column index of the sample s. This column provides the data x1, x2 etc.

Return Values

Arithmetical expression. FAIL is returned, if the kurtosis does not exist.

See Also

MuPAD Functions

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