Generating Ordered Families of Lorenz Curves by Strongly Unimodal Distributions
证明，从任意强单峰密度函数可生成一族洛伦兹曲线，且这些曲线按参数有序排列；对称密度产生对称曲线，并给出正态分布的一个相关刻画。
From any strongly unimodal density on the real line, it is possible to generate a one-parameter family of Lorenz curves. The resulting families of Lorenz curves are Lorenz ordered with respect to the indexing parameter. Symmetry of the unimodal density results in the generation of symmetric Lorenz curves. A related characterization of the normal distribution is presented.