kurtosis {semTools}

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.

Details

The excessive kurtosis computed by default is g_{2}, the fourth standardized moment of the empirical distribution of object. The population 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}} - 3,

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 ([e-mail])

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)