cumulant2moment: Convert raw cumulants to moments.
Description
Conversion of a vector of raw cumulatnts to moments.
Usage
cumulant2moment(kappa)
Arguments
kappa
a vector of the raw cumulants.
The first element is the first cumulant, which is also the first moment.
Value
a vector of the raw moments.
The first element of the input shall be the same as the first element of the output.
Details
The 'raw' cumulants \(\kappa_i\) are connected
to the 'raw' (uncentered) moments, \(\mu_i'\) via
the equation
$$\mu_n' = \kappa_n + \sum_{m=1}^{n-1} {n-1 \choose m-1} \kappa_m \mu_{n-m}'$$
# normal distribution, mean 0, variance 1n.mom <- cumulant2moment(c(0,1,0,0,0,0))
# normal distribution, mean 1, variance 1n.mom <- cumulant2moment(c(1,1,0,0,0,0))