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Credibility Weighted Estimate Calculator

Work out credibility weighted estimate instantly with clear inputs, formula shown and shareable results.

About Credibility Weighted Estimate Calculator

Small samples are noisy, so actuaries blend a group's own experience with a wider benchmark. The Bühlmann-style weight Z = n/(n + K) rises with claim volume, giving own experience more say only when there is enough of it.

Formula

Credibility blend

Estimate = Z × Observed + (1 - Z) × Expected; Z = n/(n + K)

n
Claim count
K
Credibility constant

Worked example

With the default values below, Credibility Weighted Estimate Calculator returns Credibility-Weighted Loss Ratio of 67.172%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Observed Loss Ratioaccepts 0–300 %
72 %
Expected Loss Ratioaccepts 0–300 %
65 %
Claim Countaccepts 1–1,000,000
180
Credibility Constant Kaccepts 1–100,000
400

Results

Credibility-Weighted Loss Ratio
67.172%
Credibility Weight Z
31.034%
Weight On The Expected Ratio
68.966%
Shift From The Expected Ratio
2.172%

Step by step

  1. 1Values used
  2. 2Credibility blend
  3. 3Credibility-Weighted Loss Ratio= 67.172
  4. 4Credibility Weight Z= 31.034
  5. 5Weight On The Expected Ratio= 68.966
  6. 6Shift From The Expected Ratio= 2.172

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What does the constant K represent?

The claim volume at which own experience earns 50% weight. It reflects how variable individual risks are relative to the group.

Why not use observed experience alone?

With few claims the observed ratio is mostly noise, and pricing off it would swing rates up and down without any real change in risk.

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Credibility Weighted Estimate Calculator | Calcrivo