semTools (version 0.4-11)

kurtosis: 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.

Value

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

Details

The excessive kurtosis computed is g2. The parameter excessive kurtosis $\gamma_{2}$ formula is $$\gamma_{2} = \frac{\mu_{4}}{\mu^{2}_{2}} - 3,$$ where $\mu_{i}$ 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.

References

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

See Also

• skewFind the univariate skewness of a variable
• mardiaSkewFind the Mardia's multivariate skewness of a set of variables
• mardiaKurtosisFind the Mardia's multivariate kurtosis of a set of variables

Examples

kurtosis(1:5)