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#1




Modeling loss ratio with GLM, fit frequency as Tweedie?
My boss wants to model loss ratio with GLM. I know many sources say that loss cost is best for GLM, but we need loss ratio.
I am thinking of doing a frequency/severity model where frequency = number of claims / premium and severity is as usual. The frequency component (excluding zeros) appears to be gamma distributed, so I'm thinking of modeling the entire frequency component as Tweedie. What do you all think?
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#2




So the frequency, which you are defining as # claims / premium, seems gammadistributed. Is this because the claim count (i.e., numerator) is somehow gamma distributed? Or is it something about the distribution of premium (denominator) that is resulting in a gammadistributed frequency? If the latter, I don't think using the Tweedie in your frequency GLM makes sense here. The distribution is meant to apply to the random element of your outcome  but the premium is a known quantity. I think you should look at the distribution of claim counts when determining which distribution to use (and probably go with Poisson).

#3




Guessing the reason you are using premium in the numerator is because you are predicting loss ratios?
If it were me, I'd try modeling the loss ratio directly instead. There's plenty of GLMs that produce predictions between 0 and 1. (in theory loss ratio's can be > 1, but I'd hope the premium being charged is at least >= losses in aggregate). 
#4




I would keep it simple and model the loss ratio using premium as weight.
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