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Chapter 18 Paper B

K

Kanishka

Active Member
Run the following code in R: set.seed(1); x <- sort(rpois(365,rgamma(365,20,0.01))) The number of claims reported to an insurance company for a particular type of insurance policy have been recorded every day for the last 365 days. These are listed in the vector x. On average, one in every 100 claims is rejected by the insurer as it is deemed to be fraudulent, and this rate has been constant for many years. However, the insurer now expects that the number of fraudulent claims will increase by 4% next year. Estimate the skewness of the number of claims the insurer can expect to pay next year.

I didn't understand the solution for this. Can someone please explain?
 
Hi Kanishka

Can you please be a bit more specific on which bits you don't understand?

I also recommend posting questions about the PBOR in the PBOR forum.

All the best

Andy
 
Andrew Martin said:
Hi Kanishka

Can you please be a bit more specific on which bits you don't understand?

I also recommend posting questions about the PBOR in the PBOR forum.

All the best

Andy
Click to expand...

I need help with the the entire thing. I just know the last part of calculating skewness.

Ps- I didn't know about the pbor forum. I will post my further doubts there.
Thank you.
 
Hi Kanishka

Let's say that on any given day this year that there are x claims reported to the insurer. Then, from the information in the question, 1% of those are expected to be fraudulent. So 0.01*x are expected to be fraudulent and 0.99*x are expected to be claims on which the insurer will pay out.

Next year the insurer still expects x total claims to be reported; however the expected proportion of fraudulent claims has increased from 1% to 1% * (1 + 4%) or 1.04%. So 0.0104 * x are expected to be fraudulent and 0.9896 * x (or [1 - 0.0104] * x) are claims on which the insurer will pay out. That is how the sample of claim numbers for next year is constructed.

Does that help?

Andy
 
Andrew Martin said:
Hi Kanishka

Let's say that on any given day this year that there are x claims reported to the insurer. Then, from the information in the question, 1% of those are expected to be fraudulent. So 0.01*x are expected to be fraudulent and 0.99*x are expected to be claims on which the insurer will pay out.

Next year the insurer still expects x total claims to be reported; however the expected proportion of fraudulent claims has increased from 1% to 1% * (1 + 4%) or 1.04%. So 0.0104 * x are expected to be fraudulent and 0.9896 * x (or [1 - 0.0104] * x) are claims on which the insurer will pay out. That is how the sample of claim numbers for next year is constructed.

Does that help?

Andy
Click to expand...
Yes I got what you said but in the solution, it's been given that non fraudulent claims are 0.99 *x this year and that they will remain unchanged next year. But how can that be because next year, non fraudulent claims are 0.9896*x.
 
Hi Kanishka

The question states that the total number of all claims remains unchanged, rather than the number of fraudulent claims.

I hope that clarifies it.

Andy
 
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