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IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples

Claim counts N on a motor policy in a year are Poisson with mean 0.5. Independent claims are of two kinds, each claim being a theft claim with probability 0.2. What is the probability that a policy has no theft claims in a year?

Thinning a Poisson count gives theft claims Poisson with mean 0.1, so the probability of none is e^-0.1 = 0.9048. The figure 0.6065 wrongly uses the total claim mean of 0.5.

  1. A0.9048Correct
  2. B0.6065
  3. C0.8187
  4. D0.9512
  5. 0.7788

Explanation

By thinning, theft claims are Poisson with mean 0.5×0.2 = 0.1. P(none) = e^-0.1 = 0.9048. Using e^-0.5 = 0.6065 ignores the thinning.

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