WeibullMoments: Raw and Limited Moments of the Weibull Distribution

In actuar: Actuarial Functions and Heavy Tailed Distributions

Raw and Limited Moments of the Weibull Distribution

Description

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

Usage

mweibull(order, shape, scale = 1)
levweibull(limit, shape, scale = 1, order = 1)

Arguments

order	order of the moment.
limit	limit of the loss variable.
shape, scale	shape and scale parameters, the latter defaulting to 1.

Details

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

Value

mweibull gives the kth raw moment and levweibull gives the kth moment of the limited loss variable.

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

Author(s)

Vincent Goulet [e-mail] and Mathieu Pigeon

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.

See Also

Weibull for details on the Weibull distribution and functions [dpqr]weibull.

Examples

mweibull(2, 3, 4) - mweibull(1, 3, 4)^2
levweibull(10, 3, 4, order = 2)

actuar documentation built on Aug. 9, 2025, 1:06 a.m.