actuar (version 3.3-4)

ExponentialSupp: Moments and Moment Generating Function of the Exponential Distribution

Description

Raw moments, limited moments and moment generating function for the exponential distribution with rate rate (i.e., mean 1/rate).

Usage

mexp(order, rate = 1)
levexp(limit, rate = 1, order = 1)
mgfexp(t, rate = 1, log = FALSE)

Value

mexp gives the \(k\)th raw moment,

levexp gives the \(k\)th moment of the limited loss variable, and

mgfexp gives the moment generating function in t.

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

Arguments

order

order of the moment.

limit

limit of the loss variable.

rate

vector of rates.

t

numeric vector.

log

logical; if TRUE, the cumulant generating function is returned.

Author

Vincent Goulet , Christophe Dutang and Mathieu Pigeon.

Details

The \(k\)th raw moment of the random variable \(X\) is \(E[X^k]\), the \(k\)th limited moment at some limit \(d\) is \(E[\min(X, d)^k]\) and the moment generating function is \(E[e^{tX}]\), \(k > -1\).

References

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

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.

See Also

Exponential

Examples

mexp(2, 3) - mexp(1, 3)^2
levexp(10, 3, order = 2)
mgfexp(1,2)