ExponentialSupp {actuar} | 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 |
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.
See Also
Examples
mexp(2, 3) - mexp(1, 3)^2
levexp(10, 3, order = 2)
mgfexp(1,2)