R: Finding excessive kurtosis

kurtosis {semTools} | R Documentation

## Finding excessive kurtosis

### Description

Finding excessive kurtosis (g2) of an object

### Usage

    kurtosis(object, population=FALSE)

### Arguments

`object` | A vector used to find a excessive kurtosis
`population` | `TRUE` to compute the parameter formula. `FALSE` to compute the sample statistic formula.

### Details

The excessive kurtosis computed is g2. The parameter excessive kurtosis γ_{2} formula is

γ_{2} = \frac{μ_{4}}{μ^{2}_{2}} - 3,

where μ_{i} denotes the i order central moment.

The excessive kurtosis formula for sample statistic g_{2} is

g_{2} = \frac{k_{4}}{k^{2}_{2}},

where k_{i} are the i order k-statistic.

The standard error of the excessive kurtosis is

Var(\hat{g}_2) = \frac{24}{N}

where N is the sample size.

### Value

A value of an excessive kurtosis with a test statistic if the population is specified as `FALSE`

### Author(s)

Sunthud Pornprasertmanit (psunthud@gmail.com)

### References

Weisstein, Eric W. (n.d.). Kurtosis. Retrived from MathWorld–A Wolfram Web Resource http://mathworld.wolfram.com/Kurtosis.html

### See Also

- `skew` Find the univariate skewness of a variable

- `mardiaSkew` Find the Mardia's multivariate skewness of a set of variables

- `mardiaKurtosis` Find the Mardia's multivariate kurtosis of a set of variables

### Examples

    kurtosis(1:5)

[Package semTools version 0.4-14 Index]