Normal approximation of Compound distribution

Discussion in 'CT6' started by Bharti Singla, Jan 4, 2017.

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  1. Bharti Singla

    Bharti Singla Senior Member

    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
     
  2. John Lee

    John Lee ActEd Tutor Staff Member

    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, ....
     
  3. Bharti Singla

    Bharti Singla Senior Member

    Okay got it. Thankyou sir.
     
  4. Bharti Singla

    Bharti Singla Senior Member

    .

    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.
     
  5. Bharti Singla

    Bharti Singla Senior Member

    Please anyone explain.
     
  6. Chandrima

    Chandrima Member

    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.
     

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    Last edited by a moderator: Aug 6, 2017
  7. Chandrima

    Chandrima Member

    I have got the logic behind adding 50. Inconvenience regretted.
     
  8. John Lee

    John Lee ActEd Tutor Staff Member

    No worries.
     

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