GammaSupp | R Documentation |
Raw moments, limited moments and moment generating function 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)
mgfgamma(t, shape, rate = 1, scale = 1/rate, log = FALSE)
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. |
t |
numeric vector. |
log |
logical; if |
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 >
-\alpha
.
mgamma
gives the k
th raw moment,
levgamma
gives the k
th moment of the limited loss
variable, and
mgfgamma
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.
GammaDist
mgamma(2, 3, 4) - mgamma(1, 3, 4)^2
levgamma(10, 3, 4, order = 2)
mgfgamma(1,3,2)
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