N urns are assigned m balls in a stochastic process based on a Pareto distribution. The process is as follows:
X is a Pareto random variable (xminimum = 1, alpha is a parameter) if X > N, throw the ball out Otherwise, put the ball in urn number floor(X)
Do this until m balls have been put in urns. Then rank the urns by number of balls.
What should the final distribution look like, as N and m approach infinity? Does it resemble any standard prob. distribution? Doing Monte Carlo simulations, it seems to be heavy tailed, but not a Pareto distribution. But I'm new to this - just getting my feet wet with stochastic processes.
Edit: Primary question is: What is prob. mass. function for balls in k-th urn (after ordering them). But I'm open to answers along the lines of: Look at it differently. Basic goal is - given a selection of choices, with balls assigned to them, but some choices a priori more popular, what is relationship between stochastic process and pmf of results? (And, yes, if you can't tell, I'm coming from an applied perspective... this question is a simplification of a model encountered assigning awards to favorites).