论文标题
Terrell对矩形分布的表征的离散类似物
A discrete analogue of Terrell's characterization of rectangular distributions
论文作者
论文摘要
乔治·R·特雷尔（George R. 在本说明中，事实证明，对于离散情况，相关系数仅对离散的矩形（某些有限晶格）分布而达到其最大值。 MSC：主要60E15； 62e10;中学62G30。 关键词和短语：离散的矩形分布；订单统计；哈恩多项式；皮尔逊相关系数。
George R. Terrell (1983, {Ann. Probab., vol. 11(3), pp. 823--826) showed that the Pearson coefficient of correlation of an ordered pair from a random sample of size two is at most one-half, and the equality is attained only for rectangular (uniform over some interval) distributions. In the present note it is proved that the same is true for the discrete case, in the sense that the correlation coefficient attains its maximal value only for discrete rectangular (uniform over some finite lattice) distributions. MSC: Primary 60E15; 62E10; Secondary 62G30. Key words and phrases: discrete rectangular distribution; order statistics; Hahn polynomials; Pearson coefficient of correlation.
