actuar (version 3.3-4)

WeibullMoments: 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)

Value

mweibull gives the \(k\)th raw moment and

levweibull gives the \(k\)th moment of the limited loss variable.

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

Arguments

order

order of the moment.

limit

limit of the loss variable.

shape, scale

shape and scale parameters, the latter defaulting to 1.

Author

Vincent Goulet and Mathieu Pigeon

Details

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

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)