actuar (version 0.9-3)

ExponentialMoments: Raw and Limited Moments of the Exponential Distribution

Description

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

Usage

mexp(order, rate = 1)
  levexp(limit, rate = 1, order = 1)

Arguments

order

order of the moment.

limit

limit of the loss variable.

rate

vector of rates.

Value

• mexp gives the $k$th raw moment and levexp gives the $k$th moment of the limited loss variable.

  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 $k$ limited moment at some limit $d$ is $E[\min(X, d)]$.

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004), Loss Models, From Data to Decisions, Second Edition, Wiley.

See Also

Exponential for details on the exponential distribution and functions {d,p,q,r}exp.

Examples

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