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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.

Details

The kth 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.

Value

mnorm gives the kth raw moment and mgfnorm gives the moment generating function in t.

Invalid arguments will result in return value NaN, with a warning.

Author(s)

Vincent Goulet vincent.goulet@act.ulaval.ca, Christophe Dutang

References

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

Examples

mgfnorm(0:4,1,2)
mnorm(3)

actuar

Actuarial Functions and Heavy Tailed Distributions

v3.1-2

GPL (>= 2)

Authors

Vincent Goulet [cre, aut], Sébastien Auclair [ctb], Christophe Dutang [aut], Nicholas Langevin [ctb], Xavier Milhaud [ctb], Tommy Ouellet [ctb], Alexandre Parent [ctb], Mathieu Pigeon [aut], Louis-Philippe Pouliot [ctb], Jeffrey A. Ryan [aut] (Package API), Robert Gentleman [aut] (Parts of the R to C interface), Ross Ihaka [aut] (Parts of the R to C interface), R Core Team [aut] (Parts of the R to C interface), R Foundation [aut] (Parts of the R to C interface)

Initial release

2021-03-30