Credibility Weighting

Classical (limited-fluctuation) and Bühlmann–Straub credibility weighting of subject experience against a complement.

Confidence standard (z)

Tolerance k (%)

CV of severity

Expected claim frequency

Observed claim count

Observed mean (subject)

Complement of credibility mean

Quantity	Value
Full credibility standard — frequency (n₀)	1,536.6
Full credibility standard — pure premium	2,089.8
Required exposures for full credibility	19,208
Partial credibility Z = √(n/n₀)	43.7%
Credibility-weighted estimate	1,109

Assumptions & limitations

Classical (limited-fluctuation) standards assume claim counts are approximately Poisson and target a given probability that observed experience is within ±k of the true mean.
Bühlmann/Bühlmann–Straub estimates require at least 2 groups with 2+ observations to estimate EPV and VHM; small samples yield unstable variance estimates (VHM floored at 0).
Group data are assumed independent across groups (risk classes) and i.i.d. within a group conditional on the group's hypothetical mean.