二维单位圆上均匀分布的代表点

摘要

代表点是用离散点集来代表一个连续型随机向量，其具有重要的实际意义。对于二维单位圆上均匀分布的代表点，给出两种新的构造方法。由于代表点是自洽点的一种特例，在理论上给出了二维单位圆上自洽点结构及满足自洽条件的相应方程，并通过序贯算法寻优得到其代表点。在该方法的基础上，提出另一种改进的构造方法。结果表明：这两种方法都有结构固定、便于计算等优点，且比文献中的方法有所改进。%Principal points are some discrete points representing a continuous random vector,which have important actual meanings. For the principal points of uniform distribution on the two-dimensional unit cir-cle,two new construction methods are proposed. Since principal point is a special case of self-consistent point,the theoretical structure of self-consistent points on two-dimensional unit circle and the corresponding equations of self-consistent conditions are given. Then,the principal points are obtained by some sequential algorithm. Moreover,another improved construction method is also proposed. The results demonstrate that:both methods are better than the previous methods and have the advantages of fixed structures and ease of calculation.