| 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 > -\alpha.
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)