Aggregate Claims Distribution - stumbling block (#01)

[TheresMoreToLifeThanExams]

Hi all,

This is my first ever post, so hopefully I will follow protocol and not get told off by any regulars or admins for breaking them accidentally ;-)

Ok here goes, I'm struggling to understand why Q 11.8 which depends on Q 11.5 has the solution described in the CMP.

Chapter 11 of ST8 (aggregate claim distribution models)

Question 11.5 (ok)

Agg claims: S is a compound POIS

Claim size: X is a PARETO

(Assume S is approx NORM)

Question 11.8 (??)

Agg claims: S (as per Q 11.5)

Claim size: X is a TRANS GAM

So E(S), V(S) and skew(S) are all required to parameterise the T.GAM then solve using the Chi-Sqr distn tables.

However, the solution for Q 11.8 appears to suggest the correct solution involves finding the 3rd moment (about 0) of X = E(X^3) rather than E(S^3) to ultimately solve for the coefficient of skewness for S.

Can anyone here help point me in the right direction please? It's probably something really obvious that I'm just not seeing right now.

Thanks in advance

Happy studying!

TMTLTE

 

[LastHurdles]

Ahh yes there is a slight trick to the solution.

Skewness is defined as the third moment about the mean i.e. the third central moment.

For a compound poisson, the third central moment is the third moment (E(X^3)) multiplied by the poisson parameter (page 16 of tables)

So instead of making the coefficient of skewness under the T.Gamma and Compound Poisson the same, we equate the Skewness under the two distributions and then solve the three simultaneos equations (mean, variance, skewness) in the usual way

 

[TheresMoreToLifeThanExams]

That's a great explanation

Thanks Last Hurdles, very impressed with your promptness of reply. Much appreciated!