buhlmannStraub: Buhlmann-Straub credibility model

Description

Fit a credibility model using the Buhlmann-Straub model.

Usage

buhlmannStraub(
  Yijt,
  wijt,
  MLFj,
  data,
  muHat = NULL,
  type = c("additive", "multiplicative"),
  returnData = FALSE
)

Value

An object of type buhlmannStraub with the following slots:

call: the matched call
type: Whether additive or multiplicative credibility model is used.
Variances: The estimated variance components. Sigma is the estimated within-group variance, and Tau is the estimate of the between-group variance.
Means: The estimated averages at the portfolio level (collective premium \(\hat{\mu}\)) and at the cluster level (weighted average \(\bar{Y}_j\)).
Weights: The total weights \(w_j\) for each cluster.
Credibility: The credibility factors \(z_j\) for each cluster.
Premiums: The collective premium \(\hat{\mu}\) and individual premiums \(\hat{V}_j\) for each cluster.
Relativity: The estimated random effects \(\hat{U}_j\) of each cluster.
RawResults: Object of type data.table with all intermediate results.
fitted.values: the fitted mean values, resulting from the model fit.

Arguments

Yijt: variable name of the response variable.
wijt: variable name of the exposure weight.
MLFj: variable name of the risk class or cluster.
data: an object that is coercible by as.data.table, containing the variables in the model.
muHat: estimate for the collective premium (portfolio mean). Default is NULL and in this case, the credibility-weighted estimator is used.
type: specifies whether the additive or multiplicative formulation of the credibility model is used. Default is additive.
returnData: Logical, indicates whether the data object has to be returned. Default is FALSE.

References

Buhlmann, H. and Straub, E. (1970). Glaubwurdigkeit fur Schadensatze. Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker, 70, 111-133.

Buhlmann, H. and Gisler, A. (2005). A Course in Credibility Theory and its Applications. Springer.

Examples

Run this code

library(actuar)
library(actuaRE)
data("hachemeister", package = "actuar")
# Prepare data
X = as.data.frame(hachemeister)
Df = reshape(X, idvar = "state",
             varying = list(paste0("ratio.", 1:12), paste0("weight.", 1:12)),
             direction = "long")
# Fit Buhlmann-Straub model
fitBS = buhlmannStraub(ratio.1, weight.1, state, Df)
summary(fitBS)
# Compare with actuar package
fit <- cm(~state, hachemeister, ratios = ratio.1:ratio.12,
          weights = weight.1:weight.12)
summary(fit)