# proc genmod/inverse gaussian

#### nassima

##### New Member
Hello everyone,

By estimating the count data (number of claims per insured) with an inverse Gaussian distribution by the GENMOD procedure SAS, SAS does not take the zero (0) data. Indeed for the dependent variable (number of claims) many contract have a number of claims 0. when I execute the GENMOD procedure with a IG distribution (inverse Gaussian ) these data are not considered (Invalid Response Values).

how do I do in this case to ensure that SAS uses all data including where zero variable for the inverse Gaussian distribution?

thank you in advance
Nassima

#### Dason

##### Ambassador to the humans
Why are you using inverse Gaussian when you have count data? As you've already noticed 0 isn't even in the support of the inverse Gaussian and it's a continuous distribution. Why not give something like the negative binomial a try?

#### nassima

##### New Member
In fact I want to model the number of claims by two models: Negative binomial and inverse Gaussian and then compared the two results
for the negative binomial I got the resultat from the GENMOD procedure. but for InverseGaussian I have the problem where the number claims equal to zero

#### GretaGarbo

##### Human
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.