moment2cumulant {PDQutils} | R Documentation |
Convert moments to raw cumulants.
Description
Conversion of a vector of moments to raw cumulants.
Usage
moment2cumulant(moms)
Arguments
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. |
Details
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.
Value
a vector of the cumulants. The first element of the input shall be the same as the first element of the output.
Note
The presence of a NA
or infinite value in the input
will propagate to the output.
Author(s)
Steven E. Pav shabbychef@gmail.com
See Also
Examples
# 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))