R: Raw and Limited Moments of the Beta Distribution

BetaMoments {actuar} | R Documentation

## Raw and Limited Moments of the Beta Distribution

### Description

Raw moments and limited moments for the (central) Beta distribution with parameters `shape1` and `shape2`.

### Usage

    mbeta(order, shape1, shape2)
    levbeta(limit, shape1, shape2, order = 1)

### Arguments

`order` | order of the moment.
`limit` | limit of the loss variable.
`shape1, shape2` | positive parameters of the Beta distribution.

### 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 > -shape1.

The noncentral beta distribution is not supported.

### Value

`mbeta` gives the kth raw moment and `levbeta` 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

`Beta` for details on the beta distribution and functions `[dpqr]beta`.

### Examples

    mbeta(2, 3, 4) - mbeta(1, 3, 4)^2
    levbeta(10, 3, 4, order = 2)

[Package actuar version 3.1-2 Index]