ON THE DISTRIBUTION OF THE RANK CORRELATION COEFFICIENT-TAU WHEN THE VARIATES ARE NOT INDEPENDENT
成果类型：
Article
署名作者：
HOFFDING, W
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2332432
发表日期：
1947
页码：
183196
关键词：
摘要：
Kendall in 1938 obtained the sampling distribution of [tau] from a universe in which all possible rankings are equally likely and showed that the distribution is asymptotically normal. In terms of the probabilities [rho], that 2 members (x 1, y 1) and (x 2, y 2) of the universe are concordant (they are concordant when (x 1[long dash]x 2) (y 1[long dash]y 2) > 0) and [kappa], that of 3 members one is concordant with the other 2, it is shown that the distribution of [tau] is asymptotically normal, provided only that the marginal distributions of x and y are continuous and [kappa][long dash][rho]2 > 0. The variance of [rho]'', the probability of concordance in a sample, is calculated for the above continuous case and also for the finite case in which all values of x and of y are different. Unbiased estimates from the samples are given in both cases.
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