Generalizing the Inequality Process’ gamma model of particle wealth statistics

Abstract

ABSTRACT The Inequality Process (IP) has been tested and confirmed against data on incomes that are approximately gamma distributed. The IP’s gamma pdf (probability density function) model expresses statistics of IP particle wealth algebraically in terms of IP parameters for the subset of IP parameters that generate approximately gamma distributions of particle wealth, a serious limitation, one leaving statistics of the many empirical distributions of income and wealth with heavier-than-gamma distribution right tails beyond algebraic expression in terms of IP particle parameters. This paper shows that an IP variance-gamma (VG) pdf model can do for the entire interval on which IP particle parameters are defined, (0,1), what the IP’s gamma pdf model does for only a subset. This paper thus generalizes the IP’s gamma pdf model, and it does so with no loss of parsimony since the IP’s VG pdf model is, like the IP’s gamma pdf model, expressed in terms of IP particle parameters.