R: Moments and Moment generating function of the Normal...

NormalSupp {actuar} | R Documentation

## 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.

### See Also

`Normal`

### Examples

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

[Package actuar version 3.1-2 Index]