actuar (version 2.3-3)

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(t, mean = 0, sd = 1, log = FALSE)

Arguments

order

vector of integers; order of the moment.

mean

vector of means.

sd

vector of standard deviations.

t

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 t.

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 \(E[e^{tX}]\).

Only integer moments are supported.

References

Johnson, N. L. and Kotz, S. (1970), Continuous Univariate Distributions, Volume 1, Wiley.

See Also

Normal

Examples

# NOT RUN {
mgfnorm(0:4,1,2)
mnorm(3)
# }