Developments in rank correlation procedures for trend detection in the analysis of water quality parameters.

摘要

lgorithms for enumerating the exact null distributions of Kendall's S and Spearman's D statistics, when there are ties in one or both of the rankings, are presented. An expression, which is used to provide a simple proof of the asymptotic normality of the score S when both rankings are tied, is obtained for the cumulant generating function of S. The usefulness of an Edgeworth approximation to the null distribution of S in the general case of tied rankings is investigated and compared with the standard normal approximation.;Exact and asymptotic results are developed for the distribution of Kendall's partial rank correlation statistic ;An asymptotic variance estimator for