Biró Tamás S, Telcs András, Jakovác Antal
HUN-REN Wigner Research Centre for Physics, 1121 Budapest, Hungary.
Hungarian Physics Department, Physics Faculty, University Babeş-Bolyai, 400084 Cluj-Napoca, Romania.
Entropy (Basel). 2024 Feb 22;26(3):185. doi: 10.3390/e26030185.
We explore formal similarities and mathematical transformation formulas between general trace-form entropies and the Gini index, originally used in quantifying income and wealth inequalities. We utilize the notion of gintropy introduced in our earlier works as a certain property of the Lorenz curve drawn in the map of the tail-integrated cumulative population and wealth fractions. In particular, we rediscover Tsallis' -entropy formula related to the Pareto distribution. As a novel result, we express the traditional entropy in terms of gintropy and reconstruct further non-additive formulas. A dynamical model calculation of the evolution of Gini index is also presented.
我们探索了一般迹形式熵与基尼指数之间的形式相似性和数学变换公式，基尼指数最初用于量化收入和财富不平等。我们利用了在我们早期工作中引入的“基尼熵”概念，它是在尾部积分累积人口和财富分数图中绘制的洛伦兹曲线的某种性质。特别是，我们重新发现了与帕累托分布相关的Tsallis熵公式。作为一个新的结果，我们用基尼熵来表示传统熵，并进一步重构了非加性公式。我们还给出了基尼指数演化的动力学模型计算。
