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April 2006 Question 8 (ii) & (iii)

Discussion in 'CT6' started by Paapi, Sep 20, 2012.

  1. Paapi

    Paapi Member

    For part(ii:confused: ) you are asked to calculate the posterior distribution of theta.
    I thought you would derive the posterior the normal way wich is prior multiplies by the likelihood interms of x (as is always the case).
    But here they have taken X = total number of claims in year i = n1Y1/c, and then shown the likelihood interms of this new X = n1Y1 /c

    How do you know that you need to use this result of X?

    In part (iii) The first line to this solution is -

    E(Y|y1,y2) = c(1+ r)^2 * E(X3|y1,y2)

    Whats the logic behind this result?? This question seems to be the hardest in the paper.
     
    Paapi, Sep 20, 2012
    #1
  2. John Lee

    John Lee ActEd Tutor Staff Member

    This was a messy question. I do recommend our ASET or revision notes (from which I copy bits of this).

    How would you know? It's not clear - but it does say given y1 and y2 where the Yi's are the total claim amounts but we have the number of claims has a Poisson.

    For year one:

    • the average total claim amount per policy was y1
    • the overall total claim amount for the whole group was y1n1
    • the overall total number of claims was y1n1/c (as each claim is c)

    So X1 = y1n1/c ~ Poi(n1θ)

    Similarly since claims are (1+r) more expensive in year 2 we will have:

    X2 = y2n2/c(1+r) ~ Poi(n2θ)

    And for year 3 we will have:

    X3 = y3n3/c(1+r)² ~ Poi(n3θ)
     
    John Lee, Sep 21, 2012
    #2

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