bstraub computes structure parameters estimators in the
B�hlmann-Straub credibility model and predict.bstraub computes
the credibility premiums.bstraub(ratios, weights,
method = c("unbiased", "iterative"),
tol = sqrt(.Machine$double.eps), maxit = 100,
echo = FALSE, old.format = TRUE)## S3 method for class 'bstraub':
predict(object, levels = NULL, newdata, \dots)
## S3 method for class 'bstraub.old':
predict(object, \dots)
"unbiased" for the
usual B�hlmann-Straub estimator, "iterative" for the
Bischel-Straub estimator (see below).TRUE, return results in the
deprecated pre-0.9-4 format."bstraub".bstraub with old.format = TRUE , an object of
class "bstraub.old". This format is
deprecated. An object of class "bstraub.old" is a list with the
following components:bstraub with old.format = FALSE, an object of
class "bstraub". An object of class
"bstraub" is a list with the following components:NULL.predict.bstraub, a vector of credibility premiums.heterogeneity =
"unbiased") of the between contracts heterogeneity parameter is
$$\hat{a} = c \left( \sum_{i = 1}^I w_{i\cdot} (X_{iw} - X_{ww})^2 -
(I - 1)\hat{s}^2 \right),$$
where $c = w_{\cdot\cdot}/(w_{\cdot\cdot}^2 - \sum_{i = 1}^I
w_{i\cdot}^2)$ and $I$ is the
number of contracts. The Bishel-Straub pseudo-estimator (heterogeneity =
"iterative") is obtained recursively as the solution of
$$\hat{a} = \frac{1}{I - 1} \sum_{i=1}^I z_i (X_{iw} - X_{zw})^2.$$
The fixed point algorithm is used with a relative error of tol
as stopping criteria.
cm instead.
The credibility premium of contract $i$ is given by
$$z_i X_{iw} + (1 - z_i) X_{zw},$$
where
$$z_{i} = \frac{w_{i\cdot} \hat{a}}{w_{i\cdot} \hat{a} + \hat{s}^2},$$
$X_{iw}$ is the weighted average of the ratios of contract
$i$, $X_{zw}$ is the weighted average of the matrix of
ratios using credibility factors and $w_{i\cdot}$ is
the total weight of a contract. $\hat{s}^2$ is the estimator
of the within contract heterogeneity and $\hat{a}$ is the
estimator of the between contract heterogeneity. Missing data are represented by NA in both the matrix of ratios
and the matrix of weights. The function can cope with complete lines
of NA in case a contract has no experience.
bstraub computes the structure parameters estimators and
returns an object of class "bstraub". The methods of
predict compute the credibility premiums.
Goovaerts, M. J. and Kaas, R. and van Heerwaarden, A. E. and Bauwelinckx, T. (1990), Effective actuarial methods, North-Holland.
cmdata(hachemeister)
## Credibility premiums calculated with the iterative estimator
fit <- bstraub(hachemeister[, 2:13], hachemeister[, 14:25],
old.format = FALSE)
fit # a list
predict(fit) # credibility premiumsRun the code above in your browser using DataLab