actuar (version 0.9-3)

GammaMoments: 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.

Value

• mgamma gives the $k$th raw moment and levgamma gives the $k$th moment of the limited loss variable.

  Invalid arguments will result in return value NaN, with a warning.

Details

The $k$th raw moment of the random variable $X$ is $E[X^k]$ and the $k$ limited moment at some limit $d$ is $E[\min(X, d)]$.

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)