Pareto Distribution of the Forbes Billionaires

The Pareto distribution is commonly used to represent situations where a small portion of the population controls a disproportionately large share of resources, such as income or wealth distribution. Our study analyzed the Forbes Billionaire List from 2001 to 2023 by fitting it to a Pareto distribution using the Maximum Likelihood Estimation (MLE). Our results showed that the distribution parameter alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} consistently ranged from 1.0 to 1.5. When the distribution parameter alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} is less than 2, the underlying Pareto distribution has infinite variance, complicating the comparisons of deviations. To address this, we used Mean Absolute Deviation MAD (about median) as an alternative approach to estimate alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}. Using MAD resulted in a three times lower root-mean-square error than using MLE. We considered MAD-based kurtosis and skewness by analogy with quantile statistics. We derived new interpretations for these measures in terms of areas of appropriately folded cumulative distribution functions. We applied this innovative approach to the Forbes Billionaire dataset, focusing on various segments, including continents, gender, and industries. We examined historical trends and considered future predictions. Our findings suggest that MAD is more effective for analyzing datasets that follow Pareto distributions.