I would like to solve a problem similar to the multinominal distribution (http://en.wikipedia.org/wiki/Multinomial_distribution):
- For k independent trials each of which leads to a success for exactly one of n categories, I would like to know the distribution of the absolute values (or modulus - http://en.wikipedia.org/wiki/Absolute_value) of the categories.
- The fixed success probability of each category is 1/n.
My model as an urn problem:
- n colored balls - all of different color
- k draws (ball is placed back in the urn)
What is the probability, that I drew balls of just one color (the same ball k times); what is the probability that I drew balls of exactly two different (arbitrary) colors; .. three different (arbitrary) colors; and so on.
The multinominal distribution does not fit as it gives the probability of any particular combination of numbers of successes for the various categories and not the absolute values of categories. Our model is a bit simplified, as the success probability of all categories is the same.
Is there a distribution describing my model?