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.

中文翻译：

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Terrell 对矩形分布的表征的离散模拟

George R. Terrell (1983, {Ann. Probab., vol. 11(3), pp. 823--826) 表明，来自大小为 2 的随机样本的有序对的 Pearson 相关系数最多为 1-一半，只有矩形（在某个区间上均匀）分布才能达到相等。在本说明中，证明了对于离散情况也是如此，因为相关系数仅在离散矩形（在某些有限格上均匀）分布时才达到最大值。MSC：初级 60E15；62E10; 次要 62G30。关键词和短语：离散矩形分布；订单统计；哈恩多项式；皮尔逊相关系数。