# Poisson process

#### kulstudent

##### New Member
Dear statisticians,

I have a question that is of great importance for my master thesis in insurance science. I have obtained a dataset that records the aggregate claim size per individual in connection to health care insurance for a certain policy year. What I do not observe, however, is the number of claims that the individuals effectively made.

Now---for a reason that is too complex to explain---I want to model claim size (per individual) in terms of "times that the individual claimed 50 dollar". My question therefore is: could this ("the number of times that an individual's cumulative health care cost exceeds a multiplicity of 50") possibly be interpreted as a Poisson process? And if not, is there another frequency distribution that could address this issue?

#### rogojel

##### TS Contributor
hi,
you could look at the mean and the variance. For a poisson distribution they should be about equal.
BTW there are several other distributions that could come into play - binomial, negative binomial ..etc. It could also happen that you have too many zeroes for the data to fit into a standard distribution .. so, best would be to show a sample of your data.

regards

#### hlsmith

##### Less is more. Stay pure. Stay poor.
"the number of times that an individual's cumulative health care cost exceeds a multiplicity of 50"

You mean is > than \$50 right? Because the above line reads differently than that.

What does the histogram of the outcome look like?

As rogojel alluded to, the selected distribution is linked to the dispersion around the mean, mean, and also sample size. With a large enough sample size, many distributions can be approximated using the normal distribution.