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IAI Actuarial Core Principles · Actuarial Statistics · Credibility theory: Bayesian and empirical Bayes credibility premiums

The proportion p of policies that lapse in a year has a Beta(2, 8) prior. In a sample of 20 policies, 6 lapse. Under quadratic (squared error) loss, what is the Bayes estimate of p?

The Bayes estimate is 0.267. The posterior is Beta(8, 22) after adding 6 lapses and 14 non-lapses to the prior parameters, and under squared error loss the estimate is the posterior mean 8/30.

  1. A0.250Correct
  2. B0.300
  3. C0.200
  4. D0.267
  5. 0.233

Explanation

The posterior is Beta(2 + 6, 8 + 14) = Beta(8, 22). Under quadratic loss the Bayes estimate is the posterior mean, 8/30 = 0.267. Option 0.300 is the sample proportion and 0.200 is the prior mean.

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