NOTE: I purposely did not label the axis due to pending publications. The line colors represent the same data in all three plots.
I fitted my data using a negative binomial distribution to generate a pdf. I am happy with the pdf and meets my research needs. PDF plot:
For when reporting the CDF, should I use the empirical or fitted CDF? There are slight differences between the empirical and fitted CDF, specifically at x = 40, the yellow and cyan lines intersect in the empirical distribution, but not the fitted.
Empirical:
Negative Binomial CDF:
Best Answer
Personally, I'd favour instead showing the fit of the theoretical to the empirical distribution using a set of P-P plots or Q-Q plots.