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Estimating Wealth Distribution in Society Using Bose-Einstein Statistics

This document presents a model designed by Dr. Willy H. Gerber to estimate the wealth distribution within a society based on the Bose-Einstein statistics framework. The model theorizes that if well-being is primarily linked to wealth, it can follow a distribution characterized by parameters such as minimum and maximum wealth levels, represented as ε_min and ε_max. Through mathematical formulation and integration, it aims to define the probability of individuals' wealth holdings, thus providing a quantitative method for analyzing economic disparities in society.

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Estimating Wealth Distribution in Society Using Bose-Einstein Statistics

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  1. SEE Wealth Distribution (Version 1.0.0) Dr. Willy H. Gerber Abstract: Model to estimate the wealth distribution in a society with the SEE model. www.gphysics.net–UACH-SEE-Wealth-Distribution-Version-1.0.0

  2. Boson Einstein Statistic If I consider that the wellbeing is mostly wealth we will have a Bose Einstein distribution: -βnsεs + α e Σ ns 1 ns ns= (0,1,2,3,4,…) ns = = -βnsεs + α e -βεs + α e Σ − 1 ns α is in physics the “chemical potential” and has to be chosen to fulfill: Σi N = ni www.gphysics.net–UACH-SEE-Wealth-Distribution-Version-1.0.0

  3. Boson Einstein Statistic If I assume that the wealth has a minimum εmin of and a maximum of εmax the probability to find a person having wealth between εand ε + dεis: dε εmax− εmin 1 dε εmax− εmin εmin≤ε ≤εmax n(ε) = -βε+ α e − 1 α is in physics the “chemical potential” and has to be chosen to fulfill: εmax ⌠ 1 dε εmax− εmin = N ⌡ -βε+ α e − 1 εmin www.gphysics.net–UACH-SEE-Wealth-Distribution-Version-1.0.0

  4. Boson Einstein Statistic Integrating: −βεmax+ α e 1 β(εmax− εmin) − 1 N = − 1 − ln −βεmin+α e − 1 and −(N+1)β(εmax − εmin) e βεmax e + α βεmax 1 − e e γ = = −Nβ(εmax− εmin) e 1 − with N >> 1 βεmax e e + α α ≈βεmax and ≈ www.gphysics.net–UACH-SEE-Wealth-Distribution-Version-1.0.0

  5. Boson Statistics Wages distribution (US) Data: OES statistics for the US market in 2005 www.gphysics.net–UACH-SEE-Wealth-Distribution-Version-1.0.0

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