How to guess a curve distribution from count data

I have a sample composed by 2500 count data values. I've plotted in R the corresponding histogram and ecdf. I've run the One-Sample Kolmogorov-Smirnov test to check if the distribution is either exponential or poisson, but I got negative results.

Is it possible that the One-Sample Kolmogorov-Smirnov test, it's not the correct test to work with this count data.

What is the best way to identify a distribution for this kind of data? • It's hard to tell from the graphs, but are there a whole lot of 0s? Mar 31 '14 at 18:31
• KS test and many others will be more likely to reject as the sample grows, unless the underlying phenomenon is very stable, like radioactive decay. Mar 31 '14 at 19:20
• Please tell us why you are attempting to characterize these data with a parametric distribution in the first place: what is the objective of your analysis?
– whuber
Mar 31 '14 at 21:06
• The exponential is continuous. Count data is discrete. You can rule out the exponential as a distribution for counts before you start. What are you trying to achieve here? Mar 31 '14 at 22:06
• yes, there are many 0s. Basically, I have a sample composed by values representing the number of users with write permissions per project. The objective of my analysis is two-fold: 1) identify a curve that could approximate my sample 2) depending on the type of distribution identified, I would like to run some correlation tests between the number of users per project and other project features. Currently, I'm checking the correlation with the Spearman's rank correlation coefficient, but I'm not sure that it is the correct test, since I don't know the curve distribution of my sample Apr 1 '14 at 8:02