Insurance calculators
Credibility and experience rating
Full credibility standard and partial credibility, Bühlmann credibility estimated from data, and the credibility-weighted premium.
Inputs
Results
Full credibility standard
1,082 claims
Credibility Z
60.8%
Credibility-weighted rate
0.6926
Methodology
Conventions
- Limited fluctuation: full credibility when the claim count gives an estimate within ±k of its mean with probability p, allowing for severity variation by its coefficient of variation. Partial credibility uses the square-root rule.
- Bühlmann: rows are risks and columns are years, with equal exposure. EPV is the average within-risk variance and VHM the variance of the risk means less EPV/n.
References
- Klugman, Panjer and Willmot, Loss Models: From Data to Decisions, 5th ed.
- Herzog, Introduction to Credibility Theory.
Formulas
- Full credibility standard
- n_F = \big(z_{(1+p)/2} / k\big)^2 (1 + CV^2)
- Partial credibility
- Z = \min\big(1, \sqrt{n / n_F}\big)
- Bühlmann
- Z = \frac{n}{n + k},\quad k = \frac{EPV}{VHM}
- Credibility premium
- P = Z\,\bar X + (1 - Z)\,M