semTools (version 0.5-4)

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)

# }