Cumulant Generating Function and Tail Probability Approximations for Kendall's Score with Tied Rankings
含并列排名的 Kendall 得分：累积量生成函数与尾概率近似
Robillard's approach to obtaining an expression for the cumulant generating function of the null distribution of Kendall's $S$-statistic, when one ranking is tied, is extended to the general case where both rankings are tied. An expression is obtained for the cumulant generating function and it is used to provide a direct proof of the asymptotic normality of the standardized score, $S/ \sqrt{\operatorname{Var}(S)}$, when both rankings are tied. The third cumulant of $S$ is…