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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).

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    Or, in general: What relationship is there between the random distribution of balls in an urn process, and the distribution of total balls collected in ranked urns? Under what conditions will they be the same? Under what conditions will they both be power laws?2011-02-28
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    What is the output of this process? As described, it seems to be an ordered list of $N$ non-negative integers adding up to $m$.2011-02-28
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    Yes, Henry, that's exactly correct. I'm interested in the distribution of those integers. What is prob. mass func. of integer x?2011-02-28
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    This seems inconsistent. If the output of the process is an ordered list of $N$ non-negative integers, what did you mean by "it seems to be [...] not a Pareto distribution"? A list of integers couldn't have a Pareto distribution, since a Pareto random variable is real-valued. Do you mean the number of balls in some individual urn? If so, which one? In any case, I suspect that ranking the urns by the number of balls will probably make the problem very complicated.2011-02-28
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    Maybe you want to throw out balls when $X>N+1$, otherwise, the $N$th urn will almost surely be empty.2011-02-28

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