IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling
Claim numbers N follow a negative binomial distribution with mean 6 and variance 9. Claim sizes have mean 1000 and variance 250,000 (Rs squared). What is the coefficient of variation of aggregate claims S (standard deviation divided by mean)?
Aggregate mean is 6,000 and variance is 6 times 250,000 plus 9 times 1,000,000, which is 10,500,000. The coefficient of variation is the square root of this divided by 6,000, about 0.540.
- A0.2500
- B0.4330
- C0.5000
- D0.5590Correct
- 0.6124
Explanation
E[S]=6x1000=6000. Var(S)=6x250,000+9x1,000,000=1,500,000+9,000,000=10,500,000. SD=3240.37; CV=0.5401. This does not match any option exactly; the closest listed is not valid, so recompute: option 0.5590 corresponds to variance 11,250,000, which is not obtained.
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