Clark vs. England/Verrall

[Bobby]

I'm getting confused when comparing the models of Clark and England/Verrall.

Clark estimates the payment (or reporting) pattern using a growth function modeled with a Weibull or Loglogistic curve. Then he says the ultimate reserves follow an over-dispersed Poisson distribution.

England/Verrall also use an over-dispersed Poisson distribution to replicate the Chain Ladder method, but don't use a Weibull or Loglogistic to model the payment pattern.

Couldn't Clark get to an over-dispersed Poisson without the Weibull/Loglogistic curve? It appears that he fits a Weibull/Loglogistic curve without even taking the Poisson distribution into consideration. Why do we even need an over-dispersed Poisson distribution here? Is it just to get a variance estimate? Couldn't we get that somehow from the Weibull/Loglogistic curve? Maybe it doesn't fit as well?

Are the Clark and England/Verrall models equivalent?

[TwoStep]

I was wondering about this too. I think he makes the OD Poisson assumption purely for the variance. Meaning, he uses the curves to fit the reserves, but assumes variance is proportional to losses developing in the prior period.

This is just a hypothesis, and I could very well be wrong.