[Swarm-Modelling] Can you help me with a probablility question about mixtures of distributions?

[Paul Johnson]

Suppose there are 50 collections of agents. Think of these collections 
as districts in a political system.   For each collection, we have 1000 
agents.  I want each agent to have a meaningul parameter in the 
left-right political scale, and I'm thinking of using a Beta 
distribution because it is bounded and displays a wide variety of 
shapes.  I vary the parameters so that not all districts are exactly the 
same in political composition.   As a first take, I have the assumption 
that the distribution within each cluster has a "cluster-specific" 
parameter, a_k, representing the first beta parameter.  So the 
observations are B(a_k,b) for districts k=1...50.

Question: is there a distribution from which to draw a_k so that the 
combined set of all agents has a known distribution?

I've stumbled around a while and I find plenty of literature on Bayesian 
statistics and the Beta as a prior to the Binomail distribution, but I 
can't find anything about the more mundane simulation question "if I 
generate cases like so, what do I have?"

What is the proper  literature to read?

pj

--
Paul E. Johnson                       email: address@hidden
Dept. of Political Science            http://lark.cc.ku.edu/~pauljohn
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