Credibility Calculator

Calculate Limited Fluctuation and Bühlmann credibility factors for actuarial ratemaking and reserving.

Claim Count (n)

Full Credibility Standard (n_full)

Prior (Manual) Mean (μ)

Observed Mean (X̄)

Expected Process Variance (EPV)

Variance of Hypothetical Means (VHM)

Tab to move between fields

Classical Credibility (Z)

0.304

Bühlmann Credibility (Z)

0.976

Bühlmann k (EPV/VHM)2.5

Credibility-Weighted Est.$5,488.00

Prior Weight2%

Data Weight98%

How to Use This Calculator

Enter the number of observed claims or exposure units (n).
Set the full-credibility standard (e.g., 1,082 claims for frequency at the 90/10 level).
Enter the prior (manual) mean and your observed mean from experience data.
Enter the Expected Process Variance (EPV) — the average within-risk variance.
Enter the Variance of Hypothetical Means (VHM) — the between-risk variance of true means.
Review the Bühlmann k parameter (EPV/VHM) and credibility factor Z = n/(n+k).
Use the credibility-weighted estimate: Z × observed + (1−Z) × prior.

What each input means

Claim Count (n): Number of observed claims or exposure units in your experience data
Full Credibility Standard (n_full): Number of claims needed for full credibility (1,082 for frequency at 90/10 per classical standard)
Prior (Manual) Mean (μ): Industry or manual rate expected value — the complement of credibility
Observed Mean (X̄): Mean from your actual observed experience data
Expected Process Variance (EPV): Average within-risk variance of individual observations (E[s²] across risks)
Variance of Hypothetical Means (VHM): Between-risk variance of the true mean across the population (Var[μ])

Identify Input Parameters
n, n_full, μ_prior, X̄_obs, EPV, VHM
n = 100, n_full = 1082, μ_prior = $5,000, X̄_obs = $5,500, EPV = 2,500,000, VHM = 1,000,000 = 6 input(s) provided
Calculate Classical Credibility
Z = min(1, √(n / n_full))
Z = min(1, √(100 / 1082)) = 0.304
Calculate Bühlmann k Parameter
k = EPV / VHM
k = 2,500,000 / 1,000,000 = 2.5
Calculate Bühlmann Credibility
Z = n / (n + k)
Z = 100 / (100 + 2.5) = 0.976
Calculate Credibility-Weighted Estimate
Est. = Z × X̄_obs + (1 − Z) × μ_prior
Est. = 0.976 × $5,500 + 0.024 × $5,000 = $5,488
Calculate Weights
Data Weight = Z × 100%, Prior Weight = (1 − Z) × 100%
Data = 0.976 × 100%, Prior = 0.024 × 100% = Data: 98%, Prior: 2%

Engine last updated August 5, 2026. Checked against 1 independently-derived test — how we verify calculators.

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