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Distribution-free confidence intervals for \(\Pr (X_ 1<X_ 2)\). (English) Zbl 0655.62052

We review the problem of obtaining a distribution-free confidence interval for the probability (p) that one random variable is less than another independent random variable based on the two-sample uncensored Wilcoxon-Mann-Whitney statistic. The pivotal quantities used by P. K. Sen [Sankhyā, Ser. A 29, 95-102 (1967; Zbl 0173.209)] and Z. Govindarajulu [Ann. Inst. Stat. Math. 20, 229-238 (1968; Zbl 0176.486)] are modified to take into account that the variance of estimated p depends on p. A number of simulations were conducted to compare the various methods. The results suggest that the proposed modification is superior in the sense that over the entire range of p the modification generally yields values of coverage probability much closer to nominal coverage than the methods of Sen and Govindarajulu.

MSC:

62G15 Nonparametric tolerance and confidence regions
62Q05 Statistical tables
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