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)
Arguments
order
order of the moment.
limit
limit of the loss variable.
shape1, shape2
positive parameters of the Beta distribution.
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.
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 $E[min(X, d)^k]$.
The noncentral Beta distribution is not supported.
References
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2008),
Loss Models, From Data to Decisions, Third Edition, Wiley.
See Also
Beta for details on the Beta distribution and
functions {d,p,q,r}beta.