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Raw moments and moment generating function for the normal distribution with mean equal to mean and standard deviation equal to sd.
mean
sd
mnorm(order, mean = 0, sd = 1) mgfnorm(t, mean = 0, sd = 1, log = FALSE)
mnorm gives the \(k\)th raw moment and
mnorm
mgfnorm gives the moment generating function in t.
mgfnorm
t
Invalid arguments will result in return value NaN, with a warning.
NaN
vector of integers; order of the moment.
vector of means.
vector of standard deviations.
numeric vector.
logical; if TRUE, the cumulant generating function is returned.
TRUE
Vincent Goulet vincent.goulet@act.ulaval.ca, Christophe Dutang
The \(k\)th raw moment of the random variable \(X\) is \(E[X^k]\) and the moment generating function is \(E[e^{tX}]\).
Only integer moments are supported.
Johnson, N. L. and Kotz, S. (1970), Continuous Univariate Distributions, Volume 1, Wiley.
Normal
mgfnorm(0:4,1,2) mnorm(3)
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