# stats::kurtosis

Kurtosis (excess) of a data sample

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

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

## Description

`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.

## Examples

### 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:

`stats::kurtosis(%)`

## Parameters

 `x1, x2, …` The statistical data: arithmetical expressions. `s` A sample of domain type `stats::sample`. `c` 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.