Hi, hope you all doing well.

Some background. I work in the insurance industry as a pricing actuary, building statistical models.

The previous company I used to work for used WTW Emblem to build these statistical models. I now use R.

I keep having some thoughts with Poisson rate modelling (how many claims are we expecting through out 1 year).

In Emblem there was a parameter called scale parameter (or dispersion parameter) which showed how far are your mean and variance in Poisson model. It would not change the parameters it self, but it would change SE values (and perhaps significance of each variable?).

The way to bring this scale parameter to 1 was to aggregate the data and then it would change as you fit new variables.

I am now building Poisson rate model in R. I did some testing. I initially had 30,000 rows and then after aggregation I was left only with 300 or so. Coefficients did not change, but to my surprise the significance levels for variables haven't either. Does this mean that my data follows Poisson distribution to the perfection?

My question is:

- How glm() function take care of Poisson parameters? I believe it assumes its always 1? What if true scale parameter is not 1?
- how can I calculate this scale parameter?
- How can I plot a Poisson rate distribution? Should I calculate rate of accidents per policy and plot that?

Many thanks.