Suppose, we have a set of 10,000 individuals. Each individual falls into exactly one of 200 categories. [Edit: The categories are phenotypes (different potential outcomes) of the one property that is observed]. Observing the individuals, we can count for each category the number of corresponding individuals. This number is always a non-negative integer. Suppose, that around 30 categories are empty.
Now I would like the find a distribution describing the number of individuals in each category. I did some tests with a lognormal distribution using R and the qqplots seemed to perform well.
However, I did not know how to respect the zero values which are clearly forbidden for lognormal distributed data. During my tests, I modelled the 'zero' phenomenon separately.
To this purpose, I cut off the zero values and then fitted the lognormal distribution. Going reverse (i.e. generating numbers according to the original distribution), I first used random numbers from the binomial distribution with $n=1$, deciding whether I get a zero or a non-zero. Second, I used numbers from the fitted lognormal distribution for the non-zero values.
- Is the lognormal approach generally a bad idea for data with zeroes?
- How would you evaluate my approach?
- Are there better ways to find a distribution for discrete, non-negative data?