463 – SPEED: Methodological Advances in Time Series: BandE Speed Session, Part 1
The Inequality Process' PDF Approximation Model for Heavy-Tailed Financial Distributions
John Angle
The Inequality Process Institute LLC
The Inequality Process (IP) is an interacting particle system implying many empirical invariances in personal income and wealth statistics, seven maxims of economics, and five "stylized facts" of stock price volatility. The IP‘s particle parameter, omega, is the fraction of wealth (a positive quantity) an IP particle loses to a competitor particle in a loss. A gamma pdf (probability density function), whose shape and scale parameters are expressed in terms of particle omegas, approximates the stationary distribution of IP particle wealth in a particular omega equivalence class of particle if its omega < .5. This approximating gamma pdf implies scalar particle wealth statistics in that omega equivalence class, expressed in terms of particle parameters, as long as that class' omega < .5. This paper introduces an approximating variance-gamma (VG) pdf with its three parameters in terms of particle omegas, for 0.0 < omega < 1.0 . This generalization converges to the approximating gamma pdf model for omegas < .5. The VG pdf is widely used to model right skewed heavy-tailed financial distributions.