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Pareto Distribution of the Forbes Billionaires

Author

Listed:
  • Eugene Pinsky

    (Metropolitan College)

  • Weiqi Zhang

    (Metropolitan College)

  • Zibo Wang

    (Metropolitan College)

Abstract

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 $$\alpha$$ α consistently ranged from 1.0 to 1.5. When the distribution parameter $$\alpha$$ α 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 $$\alpha$$ α . 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.

Suggested Citation

  • Eugene Pinsky & Weiqi Zhang & Zibo Wang, 2025. "Pareto Distribution of the Forbes Billionaires," Computational Economics, Springer;Society for Computational Economics, vol. 66(1), pages 809-834, July.
    • Handle: RePEc:kap:compec:v:66:y:2025:i:1:d:10.1007_s10614-024-10730-1
    DOI: 10.1007/s10614-024-10730-1
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    References listed on IDEAS

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    1. Hamermesh, Daniel S. & Leigh, Andrew K., 2022. "“Beauty too rich for use”: Billionaires’ assets and attractiveness," Labour Economics, Elsevier, vol. 76(C).
    2. Wildauer, Rafael & Kapeller, Jakob, 2022. "Tracing the invisible rich: A new approach to modelling Pareto tails in survey data," Labour Economics, Elsevier, vol. 75(C).
    3. Xue, Jing-Hao & Titterington, D. Michael, 2011. "The p-folded cumulative distribution function and the mean absolute deviation from the p-quantile," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1179-1182, August.
    4. Zhang, Dayong & Hu, Min & Ji, Qiang, 2020. "Financial markets under the global pandemic of COVID-19," Finance Research Letters, Elsevier, vol. 36(C).
    5. Rytgaard, Mette, 1990. "Estimation in the Pareto Distribution," ASTIN Bulletin, Cambridge University Press, vol. 20(2), pages 201-216, November.
    6. Ma, Lin & Ruzic, Dimitrije, 2020. "Globalization and top income shares," Journal of International Economics, Elsevier, vol. 125(C).
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