Kth standardised or central moment of a distribution

kthmoment(object, k, type = "central")

Arguments

object

Distribution.

k

the kth moment to calculate

type

one of 'central', 'standard' or 'raw', abbreviations allowed

Value

If univariate, the given k-moment as a numeric, otherwise NULL.

Details

The kth central moment of a distribution is defined by $$CM(k)_X = E_X[(x - \mu)^k]$$ the kth standardised moment of a distribution is defined by $$SM(k)_X = \frac{CM(k)}{\sigma^k}$$ the kth raw moment of a distribution is defined by $$RM(k)_X = E_X[x^k]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution.

Abbreviations for the type are allowed but if an unfamiliar input is given then the central moment is computed.

Can only be used after decorating with CoreStatistics.

R6 Usage

$kthmoment(k, type = "central")

See also