How to fit a histogram by another histogram?

Dear all,
Recently, I need to fit a histogram, this is come from experiment.
To understand the relationship between this one and another histogram which come from simulation, we hope we can figure out by fit.
On my hand, I just have a curve which provided by vendor. This curve indicates the case of one photon. Then I got two, three, …, photons histograms by simulating random.
At first, I want to fit these simulated histograms with polynomial then convolute with Poisson (we assume these histograms follow Poisson distribution). However, I failed to get all histogram’s “good” function by root fit, since some of the functions have negative values. Even though, I tried to convolute them, the result is terrible of course.
Then, I tried to call the Chi2Test() function. It’s not good also.
Finally, I tried to fit the Poisson convoluted histogram to get a fit function, then use this function, limit the parameters, to fit the experiment histogram. Refer to attachment please.
The problem is, the Chi2/NDF is not so good. But I am not so sure this means the simulated histogram and the experiment one not compatible. Can anyone tell me how to improve my fit?

Thanks a lot in Advance!