Generalized Linear Models using a Tweedie Distribution

Question

We had a customer yesterday ask us about Tweedie distributions in GLM - he pointed out that JMP does not have this capability but that SPSS does.  Not a good situation, so I have a twofold question, has anyone heard of Tweedie and if so, would you mind sharing what you know?  I searched the web for references and it appears that Tweedie is a distribution used in Mix models with a Log or Identity function.

A little more on Tweedie -

"The Tweedie distribution is a member of the exponential dispersion family and thus can be used in a GLM"

I am guessing from what I have read that is GLIMMIX and that is a non-starter, but I also wanted to know if others have run into Tweedie.

Thanks,

Bill

MikeD_Anderson · Accepted Answer

Never seen it before, even in my insurance companies. Here’s a reference with a picture and a little application discussion:

http://www.statisticshowto.com/tweedie-distribution/

It looks like what makes it special is that point mass at zero… Otherwise, it appears to be just an exponential.

M

jiancao · Accepted Answer

I had an insurance customer asking about it since they deal with claims data where in a giver year most of claims are zero but some are >0. (In contrast, the Gamma distribution, which is available in JMP's GenReg, is for y>0, but doesn't supoort y≥0.)  Twedie distribution is very useful for modeling data which have positive mass at zero, but are otherwise continuous. I'd like to see it in our GenReg.

Tweedie-distribuition based models have become available in numerous SAS procedures since SAS 9.4. The following is from http://support.sas.com/kb/30/333.html:

"ln SAS/STAT, DIST=TWEEDIE option in PROC HPGENSELECT (beginning in SAS 9.4) , PROC GENMOD (beginning in SAS 9.4 TS1M1), and PROC GAMPL (beginning in SAS 9.4 TS1M5). Also SAS Viya procedures GENSELECT, GAMMOD, and SEVSELECT. Two parameterizations of the Tweedie distribution are available in SAS/ETS PROC SEVERITY beginning in SAS 9.3, in SAS/ETS PROC HPSEVERITY beginning in SAS 9.4, and in SAS Viya PROC SEVSELECT. "

brady_brady · Accepted Answer

A ZI-Gamma, which is supported by GenReg, might do a decent job of approximating the true structure, which is explained somewhat technically in the below link:

https://support.sas.com/rnd/app/stat/examples/tweedie/tweedie.pdf