Affine growth of wealth

Economists fit both the log-normal and Pareto distributions to wealth depending on whether they are on the right tail or not.

Coin flips with offset returns are approximated by the normal distribution, linear returns by the log-normal and affine returns seem to be approximated by an appropriately scaled logit-normal distribution. A good fit for income is performed by this latter distribution. Perhaps because, for some cases at least, affine returns result in power law tails. Further details for mean household incomes for US neighbourhoods are contained in a pre-print on GitHub.