Maybe reading about the

Tweedie distribution like in

this blog post by Joseph Rickert might help: "For example, one might model the insurance claims for a customer as a series of independent gamma random variables and the number of claims in some time interval as a Poisson random variable." There is also an estimation with the inverse-gaussian distribution.

\(V(\mu)= \mu^p \)

"Some very familiar distributions fall into the Tweedie family. Setting p = 0 gives a normal distribution. p = 1 is Poisson. p = 2 gives a gamma distribution and p = 3 yields an inverse Gaussian. However, much of the action for fitting Tweedie GLMs is for values of p between 1 and 2. In this interval, closed form distribution functions don’t exist, but as it turns out, Tweedies in this interval are compound Poisson distributions. (A compound Poisson random variable Y is the sum of N independent gamma random variables where N follows a Poisson distribution and N and the gamma random variates are independent.)"

So the Tweedie distribution seems to be a very useful and versatile distribution. (This could also have the extra benefit of moving from sas towards R.)

But i notice that

sas also has something about Tweedie (to my surprice).

But maybe the OP just used the number of claims. Then it seems more natural with Poisson or negative binomial.