NormalSupp: Moments and Moment generating function of the Normal Distribution
Description
Raw moments and moment generating function for the normal distribution with
mean equal to mean and standard deviation equal to sd.
Usage
mnorm(order, mean = 0, sd = 1)
mgfnorm(x, mean = 0, sd = 1, log = FALSE)
Arguments
order
vector of integers; order of the moment.
mean
vector of means.
sd
vector of standard deviations.
x
numeric vector.
log
logical; if TRUE, the cumulant generating function
is returned.
Value
mnorm gives the $k$th raw moment and
mgfnorm gives the moment generating function in x.
Invalid arguments will result in return value NaN, with a warning.
Details
The $k$th raw moment of the random variable $X$ is
$E[X^k]$ and the moment generating function is
$E[e^{xX}]$.
Only integer moments are supported.
References
Johnson, N. L. and Kotz, S. (1970), Continuous univariate
distributions, Volume 1, Wiley.