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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling

Which statement about the number of claims N in a compound distribution is correct?

The negative binomial distribution has variance exceeding its mean, so it is appropriate for overdispersed claim counts. The Poisson has equal mean and variance, while the binomial has variance smaller than its mean.

  1. APoisson has variance less than its mean, binomial has variance equal to its mean
  2. BNegative binomial has variance greater than its mean, so it suits overdispersed claim countsCorrect
  3. CBinomial has variance greater than its mean, so it suits overdispersed claim counts
  4. DPoisson has variance greater than its mean, so it suits overdispersed claim counts
  5. Negative binomial has variance equal to its mean, like the Poisson

Explanation

Poisson has variance equal to mean, binomial has variance below its mean (npq<np), and negative binomial has variance above its mean. Hence the negative binomial is used when claim counts are more variable than Poisson.

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