Department of Banking and Finance, Faculty of Commerce and Accountancy, Chulalongkorn University, Mahitaladhibesra Bld., 10th Fl., Phayathai Rd., Pathumwan, Bangkok, 10330, Thailand.
Department of Chemical Engineering, Faculty of Engineering, Khon Kaen University, Mittapap Rd., Muang District, Khon Kaen, 40002, Thailand.
Sci Rep. 2023 Mar 23;13(1):4729. doi: 10.1038/s41598-023-31827-x.
Given that the existing parametric functional forms for the Lorenz curve do not fit all possible size distributions, a universal parametric functional form is introduced. By using the empirical data from different scientific disciplines and also the hypothetical data, this study shows that, the proposed model fits not only the data whose actual Lorenz plots have a typical convex segment but also the data whose actual Lorenz plots have both horizontal and convex segments practically well. It also perfectly fits the data whose observation is larger in size while the rest of observations are smaller and equal in size as characterized by two positive-slope linear segments. In addition, the proposed model has a closed-form expression for the Gini index, making it computationally convenient to calculate. Considering that the Lorenz curve and the Gini index are widely used in various disciplines of sciences, the proposed model and the closed-form expression for the Gini index could be used as alternative tools to analyze size distributions of non-negative quantities and examine their inequalities or unevennesses.
鉴于现有的洛伦兹曲线参数函数形式并不适用于所有可能的规模分布，因此引入了一种通用的参数函数形式。通过使用来自不同科学领域的经验数据以及假设数据，本研究表明，所提出的模型不仅适用于实际洛伦兹图具有典型凸段的数据，也适用于实际洛伦兹图具有水平和凸段的数据。它还非常适合于那些观测值较大而其余观测值较小且相等的情况，其特征是两个正斜率线性段。此外，所提出的模型具有基尼指数的闭式表达式，使其在计算上非常方便。考虑到洛伦兹曲线和基尼指数在科学的各个领域都得到了广泛应用，因此所提出的模型和基尼指数的闭式表达式可以作为分析非负数量规模分布并检验其不平等或不均匀性的替代工具。
