# ExponentialSupp: Moments and Moment Generating Function of the Exponential... In actuar: Actuarial Functions and Heavy Tailed Distributions

 ExponentialSupp R Documentation

## 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)
``````

### 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.

### 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`.

### 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.

### Author(s)

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

### 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.

`Exponential`
``````mexp(2, 3) - mexp(1, 3)^2