actuar (version 3.3-4)

BetaMoments: 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)

Value

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

levbeta 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.

shape1, shape2

positive parameters of the Beta distribution.

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 \(E[\min(X, d)^k]\), \(k > -\alpha\).

The noncentral beta distribution is not supported.

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)