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表示为P–P图与ROC曲线下积分的秩统计量AI 解读

Summary Given a probability measure on the unit square, the measure of the region under an empirical P–P-plot defines a two-sample rank statistic. Instances include trimmed and censored versions of the Mann–Whitney–Wilcoxon statistic and a class of statistics with applications in the analysis of receiver operating characteristic (ROC) curves. A large sample distribution for such a statistic is obtained, which is valid under sampling from general populations. Explicit results…

各向异性粒子问题的形状分析AI 解读

SUMMARY The problem of inferring the shape distribution of anisotropically oriented spheroidal particles from their elliptical traces in planar samples is addressed by generalizing a size-shape independence condition suggested by Wicksell in his original discussion of the corpuscle problem. Shape statistics are introduced through which the eccentricities of the sampled ellipses may be related to some suitably defined moments of the underlying particle shape distribution,…