Reflections on the Structure and Origin of Pareto Income Distributions

The essay takes the reader on a voyage of exploration with the aim of discovering the origin of Pareto-curves. It shows with thought-experiments backed up by computer-simulation the generation of log-normal curves in detail. Extending forward this conceptual trajectory, it arrives via a quasi-Newtonian fluxion-insight – infinitessimal differential integration – at a novel mathematical concept: Pareto-curves are simply special log-normal curves where a large number of random-factors interacted and impacted at their genesis (the author called it the Kopp-effect).     

Pareto Density Distributions

Building on new insights into the genesis ofPareto-Distributions,(“Kopp” effect etc.) as publishedearlier in “Quality and Quantity”, the author gives at least oneauthentic/definitive Pareto-Formula. A practical example of the synthetic generation of Pareto Distributions by means of spreadsheets. A working D.I.Y-method for fine-fitting Pareto-curvesto scattergrams with spreadsheets using interalia an indirect method of the least squares of residuals is fully demonstrated. A comparative test-fit to a cumulative Pareto- Distribution example, where a simulative curve-formula evolved by Prof. B. Arnold/Ucla is used for demonstration. Easy to absorb and to retain graphical tableaux are employed to visualize the chain of descent and interconnections between normal distributions, log-normal distributions and Pareto- Distributions. A quasi-dichotomy of the Pareto-formulae is presented in tableau-form. One innovative formula for Pareto-distribution is given as: F(x)= k^*e― [((ln(Integral(In(x)))) ‐ (ln(Integral(ln(μ)))))² / 2^*(ln(Integral(ln(σ))))²} Readers e-mailed constructive opinions &/or inputs are encouraged and welcomed. This revised version was published online in June 2006 with corrections to the Cover Date.