skew {semTools}

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.

Details

The skewness computed by default is g_{1}, the third standardized moment of the empirical distribution of object. The population parameter skewness \gamma_{1} formula is

\gamma_{1} = \frac{\mu_{3}}{\mu^{3/2}_{2}},

where \mu_{i} denotes the i order central moment.

The skewness formula for sample statistic g_{1} is

g_{1} = \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}_1) = \frac{6}{N}

where N is the sample size.

Value

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

Author(s)

Sunthud Pornprasertmanit ([e-mail])

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

skew(1:5)