Moments and Moment Generating Function of the Exponential Distribution
Raw moments, limited moments and moment generating function for the
exponential distribution with rate rate (i.e., mean
1/rate).
mexp(order, rate = 1) levexp(limit, rate = 1, order = 1) mgfexp(t, rate = 1, log = FALSE)
order |
order of the moment. |
limit |
limit of the loss variable. |
rate |
vector of rates. |
t |
numeric vector. |
log |
logical; if |
The kth raw moment of the random variable X is E[X^k], the kth limited moment at some limit d is E[min(X, d)^k] and the moment generating function is E[e^{tX}], k > -1.
mexp gives the kth raw moment,
levexp gives the kth 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.
Vincent Goulet vincent.goulet@act.ulaval.ca, Christophe Dutang and Mathieu Pigeon.
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.
mexp(2, 3) - mexp(1, 3)^2 levexp(10, 3, order = 2) mgfexp(1,2)
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