GammaMoments {actuar} | R Documentation |
Raw moments and limited moments for the Gamma distribution with
parameters shape
and scale
.
mgamma(order, shape, rate = 1, scale = 1/rate) levgamma(limit, shape, rate = 1, scale = 1/rate, order = 1)
order |
order of the moment. |
limit |
limit of the loss variable. |
rate |
an alternative way to specify the scale. |
shape, scale |
shape and scale parameters. Must be strictly positive. |
The kth 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)].
mgamma
gives the kth raw moment and
levgamma
gives the kth moment of the limited loss
variable.
Invalid arguments will result in return value NaN
, with a warning.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004), Loss Models, From Data to Decisions, Second Edition, Wiley.
GammaDist
for details on the Gamma distribution and
functions {d,p,q,r}gamma
.
mgamma(2, 3, 4) - mgamma(1, 3, 4)^2 levgamma(10, 3, 4, order = 2)