semTools (version 0.5-2)

kurtosis: Finding excessive kurtosis

Description

Finding excessive kurtosis (\(g_{2}\)) 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 \(g_{2}\). 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

• 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

# NOT RUN {
kurtosis(1:5)

# }