论文标题
广义洛伦兹的优势命令
Generalized Lorenz dominance orders
论文作者
论文摘要
我们通过使用非归一化洛伦兹曲线来扩展离散的主要化理论。然后，我们证明了Muirhead定理的两个概括。这些不仅使用基本传输，而且还使用局部增加。这些操作一起被描述为基本影响的增加。第一个概括表明，如果阵列x在广义上是由数组y主导的，那么y可以通过x得出有限数量的基本影响增加，并且以这样的方式将阵列转换为新的阵列，而在广义上的主要化中，该数组严格较大。另一个表明，如果对主导阵列y的排序降低，则基本影响从主导的阵列x开始增加，从而导致占主导地位。在这里，每个步骤都会将一个数组转换为一个新的阵列，该数组的降低有序版本主导了前一个，并由Y主导。
We extend the discrete majorization theory by working with non-normalized Lorenz curves. Then we prove two generalizations of the Muirhead theorem. These not only use elementary transfers but also local increases. Together these operations are described as elementary impact increases. The first generalization shows that if an array X is dominated, in the generalized sense, by an array Y then Y can be derived from X by a finite number of elementary impact increases and this in such a way that each step transforms an array into a new one which is strictly larger in the generalized majorization sense. The other one shows that if the dominating array, Y, is ordered decreasingly then elementary impact increases starting from the dominated array, X, lead to the dominating one. Here each step transforms an array to a new one for which the decreasingly ordered version dominates the previous one and is dominated by Y.
