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 2 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.

翻译：鉴于现有洛伦兹曲线的参数函数形式无法拟合所有可能的大小分布，本文引入了一种通用的参数函数形式。通过使用不同学科的经验数据以及假设数据，本研究表明，所提出的模型不仅能够良好拟合实际洛伦兹图具有典型凸线段的数据，还能有效拟合实际洛伦兹图同时包含水平线段和凸线段的数据。该模型也能完美拟合那些观测值较大而其余观测值较小且相等的数据，其特征为两条正斜率线性线段。此外，所提模型具有基尼系数的闭式表达式，使得计算在数值上更为便捷。考虑到洛伦兹曲线和基尼系数在科学各学科中的广泛应用，所提出的模型及其基尼系数闭式表达式可作为分析非负量大小分布及其不平等或不均衡程度的替代工具。