一个新的Lorenz曲线模型

Lorenz曲线为描述居民收入分布状况及财富分配不平等程度提供了一个重要工具。为了准确地刻画居民收入分布特征，提出了一个新的Lorenz曲线模型，主要包括两个方面：第一，给出一个基础Lorenz曲线，并论证了其基本性质；第二，通过加权乘积方式，构造出新的衍生Lorenz曲线模型。新Lorenz曲线模型主要有三个方面的优势：模型表示简单，具有较少的待估计参数；模型结构灵活，容易取得更好的拟合效果；模型构造开放，可进一步扩展得到新的衍生Lorenz曲线模型。最后，通过数值模拟比较与实际应用分析，发现新的衍生Lorenz曲线模型不仅比已有的10种衍生Lorenz曲线模型具有更好的拟合效果，而且能够准确地刻画居民收入分布特征。

A new Model for Lorenz Curve

The Lorenz curve provides an important tool for describing distribution and inequality of income. It is crucial to get an accuracy Lorenz curve to simulate the real data. To this end, we propose a new model for Lorenz curve. Firstly, we create a basic Lorenz curve and demonstrate its statistical properties. Secondly, we develop a new derivative model for Lorenz curve through weighted-product operation. The new model has at least three advantages. It has a simple representation with fewer parameters to be estimated. Its structure is so flexible that better fitting results can be easy to get. Moreover, the model can be extended to obtain some other new derivative Lorenz curve models due to its openness. In the end, we examine the performance of the new model through Monte Carlo simulation and real data application. The results show that our model not only outperforms some 10 types of derivative models for Lorenz curve in terms of goodness of fit, but also presents accurate simulation to household income distribution.