Fit with discrete distribution

Hello, I have a histogram which I would like to fit with a Poisson distribution. One problem is that the data which were used to fill the histogram were integers divided by some scaling factor. While the bin centers are not integers, each bin properly fenceposts the integer nature of the raw data.

I am unsure how to go about getting a reasonable fit, since the drawn distribution upon fitting is continuous, using the Gamma-function definition of the Poisson distribution.

As a simpler example of my problem, try this code:

TF1 fp("pois","TMath::Poisson(x,[0])",0,80)
TH1F h1("h1","h1",10,0,9)

I understand that a fundamental problem is that TF1 are continuous floating-point functions, not integer-valued ones, but I would like to end up with a fitted function which has steps like a real Poisson distribution. In the end I would like these steps to not be at integer values so that I can apply them to my histogram with integer/scaling values.

Thanks for any advice.


You might get more information/answers by posting on the Math and Statistics forum rather than the general support.