How do we know which of the two Negative Binomial distribtions to use? In particular, I came across a problem using them for N in compound claim distributions. For example, Q&A Bank q2.13. When I attempted this question, I used the Type 1 Negative Binomial because it gave an expected number of claims of 4.44, which I intuitively felt was more reasonable than the expected number of claims under Type 2, which was 0.44 (I know that really there is no rational reason for this!) Needless to say, the solution had used the Type 2 after all. My question is: how do we know which one the examiners will be looking for - and will we be penalised for using the wrong type? Presumably the same issue also applies to the Geometric (which is Negative Binomial with k=1)?
I was wondering about this too. I seem to find that, unless they specify othewise, they're invariably refering to the type 2 binomial distribution.
There's a really easy way to get it right every time. If you look at the formulae on Pages 8 and 9 of the Tables, you see that for Type I the possible values of x are k, k+1, k+2, .... However, for Type 2, the possible values are 0, 1, 2, .... So look at what each question tells you about the possible values of the random variable, and then make your decision. In CT6, the negative binomial is sometimes used to model the number of claims. Since it's perfectly possible to have 0 claims, Type 2 is the one to use in this situation.
Hi Resurrecting an old thread... I follow the discussion below but one aspect of using the Type 2 negative binomial distribution to model number of claims confuses me a little. I understand that this version of the negative binomial distribution is looking at the number of "failures" (= claims) before the kth success. However what exactly can we think of k as representing when a scenario is framed in this way? Thanks Simon
I could be wrong but I think it's the case that of the discrete models available for modelling the number of claims we could have a choice between the Poisson or negative binomial (as the binomial limits the number of claims which isn't appropriate for GI). But since the Poisson has equal mean and variance it may not be appropriate - hence choose the Nbin... Its origins and its application don't tie up...
