Normal approximation of Compound distribution

[Bharti Singla]

Hi all
In Risk models, three types of compound distributions are given- Compound Binomial, Compound Poisson and Compound Neg. binomial. My question is when we need to find probabilities of S, we take S is approximately normally distributed. Then should we use continuity correction while finding prob. of S?
In some qus. it is not used, two of these are:

Q&A bank part 2- Qus.2.18(iii)
Ifoa April 2009, qus. 9(ii)

however, in Ifoa April 2008, qus 10(iv) , continuity cirrection is used.

Please anyone explain.. why it is not used in these qus ?
Thanks

 

[John Lee]

You only use a continuity correction when you are using the continuous normal distribution to approximate a discrete distribution.

Claims are modelled as continuous and hence we wouldn't apply it there.

However, in april 2008 S is a discrete distribution that can only take the values 0, 100, 200, 300, ....

 

[Bharti Singla]

Okay got it. Thankyou sir.

 

[Bharti Singla]

You only use a continuity correction when you are using the continuous normal distribution to approximate a discrete distribution.

Claims are modelled as continuous and hence we wouldn't apply it there.

However, in april 2008 S is a discrete distribution that can only take the values 0, 100, 200, 300, ....

.

One more question sir:
Ifoa, April 2000, Qus.7
Here, S is discrete distribution(Since X is discrete) but continuity correction is not used in both parts (ii)-b,c. Please explain why it is not used in this qus.?
Thankyou.

 

[Bharti Singla]

.

One more question sir:
Ifoa, April 2000, Qus.7
Here, S is discrete distribution(Since X is discrete) but continuity correction is not used in both parts (ii)-b,c. Please explain why it is not used in this qus.?
Thankyou.

Please anyone explain.

 

[Chandrima]

You only use a continuity correction when you are using the continuous normal distribution to approximate a discrete distribution.

Claims are modelled as continuous and hence we wouldn't apply it there.

However, in april 2008 S is a discrete distribution that can only take the values 0, 100, 200, 300, ....

Sir, I have the similar sort of question. Please refer to CT6 IFoA April 2008's Q. 10's last portion. I am sending you the screenshots. They asked for P(S>500) and P(T>500) for compound binomial distributions. They used 550 instead of using 500.5, why? Kindly let me know. I am stuck.

 

[Chandrima]

I have got the logic behind adding 50. Inconvenience regretted.

 

[John Lee]

No worries.