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semTools (version 0.5-6)

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 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.

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

Run this code
# NOT RUN {
skew(1:5)

# }

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