GammaMoments {actuar}R Documentation

Raw and Limited Moments of the Gamma Distribution

Description

Raw moments and limited moments for the Gamma distribution with parameters shape and scale.

Usage

  mgamma(order, shape, rate = 1, scale = 1/rate)
  levgamma(limit, shape, rate = 1, scale = 1/rate, order = 1)

Arguments

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.

Details

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)].

Value

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.

Author(s)

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

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004), Loss Models, From Data to Decisions, Second Edition, Wiley.

See Also

GammaDist for details on the Gamma distribution and functions {d,p,q,r}gamma.

Examples

mgamma(2, 3, 4) - mgamma(1, 3, 4)^2
levgamma(10, 3, 4, order = 2)

[Package actuar version 0.9-3 Index]