  The classical B\"{u}hlmann credibility model has been widely applied to
premium estimation for group insurance contracts and other insurance types. In
this paper, we develop a robust B\"{u}hlmann credibility model using the
winsorized version of loss data, also known as the winsorized mean (a robust
alternative to the traditional individual mean). This approach assumes that the
observed sample data come from a contaminated underlying model with a small
percentage of contaminated sample data. This framework provides explicit
formulas for the structural parameters in credibility estimation for
scale-shape distribution families, location-scale distribution families, and
their variants, commonly used in insurance risk modeling. Using the theory of
\(L\)-estimators (different from the influence function approach), we derive
the asymptotic properties of the proposed method and validate them through a
comprehensive simulation study, comparing their performance to credibility
based on the trimmed mean. By varying the winsorizing/trimming thresholds in
several parametric models, we find that all structural parameters derived from
the winsorized approach are less volatile than those from the trimmed approach.
Using the winsorized mean as a robust risk measure can reduce the influence of
parametric loss assumptions on credibility estimation. Additionally, we discuss
non-parametric estimations in credibility. Finally, a numerical illustration
from the Wisconsin Local Government Property Insurance Fund indicates that the
proposed robust credibility approach mitigates the impact of model
mis-specification and captures the risk behavior of loss data from a broader
perspective.
