R: Raw and Limited Moments of the Weibull Distribution

WeibullMoments {actuar} | R Documentation

## 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 > -shape.

### 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 vincent.goulet@act.ulaval.ca 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)

[Package actuar version 3.1-2 Index]