Finding skewness (\(g_{1}\)) of an object
skew(object, population = FALSE)A vector used to find a skewness
TRUE to compute the parameter formula. FALSE
to compute the sample statistic formula.
A value of a skewness with a test statistic if the population is
specified as FALSE
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.
Weisstein, Eric W. (n.d.). Skewness. Retrived from MathWorld--A Wolfram Web Resource: http://mathworld.wolfram.com/Skewness.html
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