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 kkth raw moment of the random variable XX is E[Xk]E[X^k] and the kkth limited moment at some limit dd is E[min(X,d)k]E[\min(X, d)^k], k>αk > -\alpha.

The noncentral beta distribution is not supported.

Value

mbeta gives the kkth raw moment and levbeta gives the kkth 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 3.3-4 Index]