Raw and Limited Moments of the Beta Distribution
Raw moments and limited moments for the (central) Beta distribution
with parameters shape1 and shape2.
mbeta(order, shape1, shape2) levbeta(limit, shape1, shape2, order = 1)
order |
order of the moment. |
limit |
limit of the loss variable. |
shape1, shape2 |
positive parameters of the Beta distribution. |
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.
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.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.
Beta for details on the beta distribution and
functions [dpqr]beta.
mbeta(2, 3, 4) - mbeta(1, 3, 4)^2 levbeta(10, 3, 4, order = 2)
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