IAI Actuarial Core Principles · Actuarial Statistics · Credibility theory: Bayesian and empirical Bayes credibility premiums
In an empirical Bayes credibility analysis the ratio k = E[s²(θ)] / Var[m(θ)] is estimated as 5. How many years of data per risk are needed for the credibility factor to equal 0.8?
Twenty years are needed. Setting n/(n+5) = 0.8 gives n = 4/0.2 = 20. At n = 20 the credibility factor is 20/25 = 0.8, so the risk's own experience carries 80% of the weight.
- A4
- B10
- C15
- D20Correct
- 25
Explanation
Z = n/(n+5) = 0.8 gives n = 0.8n + 4, so 0.2n = 4 and n = 20. Choosing 4 comes from multiplying 0.8 by 5 instead of solving the equation.
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