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Single/Double Parameter Pareto
ASM Manual Exercise #16.21
 On an insurance coverage, loss size has the following distribution: ; The number of claims has a negative binomial distribution with mean 0.3, variance 0.6. Claim counts and loss sizes are independent. A deductible of 3000 is applied to each claim. Calculate the variance of aggregate payments.  The formula above is that of a singleparameter Pareto distribution, but the book calculates E(x) and Var(x) based on a Twoparameter Pareto with equal to 3,000. I understand why should be increased to 3,000. My question is, is that in doing so does this always convert a singleparamter into a twoparameter Pareto?
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Jim Daniel Jim Daniel's Actuarial Seminars www.actuarialseminars.com jimdaniel@actuarialseminars.com 
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I just don't know how to calculate second moments of expected loss with a deductible. It's killing me. Can anyone walk me through this problem? (I don't have the same ASM version as OP.) 
#6




That's basically what my struggle was initially. However, like it's been mentioned above, because of the deductible this becomes a twoparameter pareto with alpha staying the same and theta becoming 3,000. The formula sheets tell you how to get the second raw moment, and therefore the variance.
I've seen similar problems where the distribution is exponential. From there you just use the memoryless property of exponential distributions to get .
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#8




Do you recall what section that was? I was looking for this topic in my version of ASM yesterday & couldn't find it.
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