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When modelling income or wealth, we probably want a continuous distribution with a lower bound; statisticians have named many, but Pareto and log-normal distributions have been among the most historically popular. Many studies have tested how well these fit the data, and (when they seemed to) estimated the parameters. But is there a theoretical basis for either of these, or for any other model? I found this motivation for a Gamma distribution, but I suspect it's far from being mainstream in economics.

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