semTools (version 0.5-0)

skew: Finding skewness

Description

Finding skewness ($g_1$) of an object

Usage

skew(object, population = FALSE)

Arguments

object

A vector used to find a skewness

population

TRUE to compute the parameter formula. FALSE to compute the sample statistic formula.

Value

A value of a skewness with a test statistic if the population is specified as FALSE

Details

The skewness computed is $g_1$. The parameter skewness ${\gamma }_2$ formula is

$${\gamma }_2=\frac{{\mu }_3}{{\mu }_2^{3/2}},$$

where ${\mu }_i$ denotes the $i$ order central moment.

The excessive kurtosis formula for sample statistic $g_2$ is

$$g_2=\frac{k_3}{k_2^2},$$

where $k_i$ are the $i$ order k-statistic.

The standard error of the skewness is

$$Var({\hat{g}}_2)=\frac{6}{N}$$

where $N$ is the sample size.

References

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

See Also

• kurtosis Find the univariate excessive kurtosis of a variable

• mardiaSkew Find Mardia's multivariate skewness of a set of variables

• mardiaKurtosis Find the Mardia's multivariate kurtosis of a set of variables

Examples

# NOT RUN {
skew(1:5)

# }