Hi, The extension of the credibility formula for general distributions with mean mu and standard deviation sigma the formula given in the notes is: If I take the same approach as that in the notes I don't get this formula, I get: Which is also consistent with the previous Poisson formula/derivation. How is the formula in the notes derived?
Hi, I too would like to understand how the general formula for standards for full credibility is derived. I don't want to ignore it, whether or not it is necessary to the exams. I feel that the approach used for the Poisson cannot be readily extended, and that some other method must be used. I would have been tempted to follow the approach given for severity, but this would just give the same answer as severity. Thanks
Firstly, there is little discussion on non-Poisson claims frequency because the Poisson distribution is overwhelmingly the most natural distribution to consider: the negative binomial is an alternative for general insurance claims, but even this is only an extension of the Poisson (as the negative binomial distribution is the Poisson/Gamma mixture distribution, see Ch3 question 3.15) what other distribution would you opt for? I've spent a long time searching for the general proof myself. All the academic papers state that the proof is given in Mayerson et al. "The Credibility of the Pure Premium". See https://www.soa.org/files/pdf/C-21-01.pdf However, I've found what I believe to be the Mayerson paper (https://www.casact.org/pubs/proceed/proceed68/68175.pdf) and it only seems to discuss the full credibility for aggregate claims. Since the Mayerson paper uses a truncated series expansion to derive the non-Poisson standard for aggregate claims, perhaps a similar approach would work for frequency? You could try it and see. In any case, I think it's a waste of time to worry about this much further. As I say, I've spent ages searching for the proof and I've not found it... in which case I'd bet the examiners won't be able to find it either!
I have a similar problem to Shillington and would like to see the full derivation if anyone knows this?