moment2cumulant {PDQutils} | R Documentation |
Conversion of a vector of moments to raw cumulants.
moment2cumulant(moms)
moms |
a vector of the moments. The first element is the first moment (the mean). If centered moments are given, the first moment must be zero. If raw moments are given, the first moment must be the mean. |
The 'raw' cumulants \kappa_i
are connected
to the 'raw' (uncentered) moments, \mu_i'
via
the equation
\kappa_n = \mu_n' - \sum_{m=1}^{n-1} {n-1 \choose m-1} \kappa_m \mu_{n-m}'
Note that this formula also works for central moments, assuming the distribution has been normalized to zero mean.
a vector of the cumulants. The first element of the input shall be the same as the first element of the output.
The presence of a NA
or infinite value in the input
will propagate to the output.
Steven E. Pav shabbychef@gmail.com
# normal distribution, mean 0, variance 1
n.cum <- moment2cumulant(c(0,1,0,3,0,15))
# normal distribution, mean 1, variance 1
n.cum <- moment2cumulant(c(1,2,4,10,26))
# exponential distribution
lambda <- 0.7
n <- 1:6
e.cum <- moment2cumulant(factorial(n) / (lambda^n))