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September 14th, 2016, 01:41 PM   #1
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Super-Rich Wealth Distribution

Hi,

I am looking for a mathematical model which can accurately forecast what percentile (1-p) of a population a member with wealth w would be in, based on Gini coefficient (G). I am planning to apply it mainly only to the top end of wealth.

I have tried to use the Pareto distribution so far. What I am unsure of there, however, is what to do with the parameter x[sub]min[/sub] as described in Wikipedia's article (https://en.wikipedia.org/wiki/Pareto_distribution):

p = (x[sub]min[/sub]/w)^P

where P, the Pareto parameter, can be expressed in terms of G by a known equation.

Wikipedia describes x[sub]min[/sub] as the (necessarily positive) minimum possible value of X. How does one apply this to a real-world population? I can't imagine setting the value to $1 or less would allow for accurate predictions of top-end wealth.

The other problem is, this x[sub]min[/sub] seems to me to behave like an average rather than a minimum value. For example, in a maximally unequal society, P=1 so p = x[sub]min[/sub]/w. This predicts that 10% of the population have wealth ten times x[sub]min[/sub], 1% have wealth a hundred times x[sub]min[/sub], and so forth. But while this is a pretty unequal society by real-world standards, it is definitely not the most unequal possible - imagine a system where 10% had a wealth a hundred times the "minimum" (or, say, the average of the remaining 90%), 1% had a wealth 100^2 times the minimum, and so forth. The most unequal system would really be everyone having "minimum" wealth except one individual. But the inequality here seems to be capped much before that.

Can anyone help with my model?
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