Finding excessive kurtosis (\(g_{2}\)) of an object
kurtosis(object, population = FALSE)A value of an excessive kurtosis with a test statistic if the
population is specified as FALSE
A vector used to find a excessive kurtosis
TRUE to compute the parameter formula. FALSE
to compute the sample statistic formula.
Sunthud Pornprasertmanit (psunthud@gmail.com)
The excessive kurtosis computed by default is \(g_{2}\), the fourth
standardized moment of the empirical distribution of object.
The population 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
$$g_{2} = \frac{k_{4}}{k^{2}_{2}} - 3,$$
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.
Weisstein, Eric W. (n.d.). Kurtosis. Retrieved from MathWorld--A Wolfram Web Resource: http://mathworld.wolfram.com/Kurtosis.html
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