# kurtosis: Finding excessive kurtosis In semTools: Useful Tools for Structural Equation Modeling

## Description

Finding excessive kurtosis (g_{2}) of an object

## Usage

 1 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 g_{2}. 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

• 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

 1 kurtosis(1:5) 

semTools documentation built on Jan. 13, 2021, 8:09 p.m.