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多元容斥公式与相依随机变量的次序统计量AI 解读

A variant of the general multivariate inclusion-exclusion formula of Meyer (1969) is derived for the case where $K$ classes of events are considered and specific subsets of the events, one from each class, are related to one another by set inclusion. This result, in turn, yields a formula for the cumulative distribution function of any subset of order statistics from dependent random variables in terms of cumulative distribution functions of subsets of the unordered…

尺度未知的指数数据的 Kolmogorov–Smirnov 型检验及相关问题AI 解读

Let D^ , D^+ and D^− denote Kolmogorov-Smirnov typo one-sample statistics to test good ness of fit in the presence of unknown nuisance parameters; then the distributions of D^ , D^+ and D^− depend on the population sampled and the estimator used. Simulation has been the primary tool for studying these statistics. Recently, Durbin obtained the distributions of D^ , D^+ and D^− in terms of a Fourier transform for a wide class of underlying populations, and produced explicit…

未知尺度指数分布的 Kolmogorov–Smirnov 型检验及相关问题AI 解读

SUMMARY: Let D, D⁺ and D⁻ denote Kolmogorov-Smirnov typo one-sample statistics to test good ness of fit in the presence of unknown nuisance parameters; then the distributions of D, D⁺ and D⁻ depend on the population sampled and the estimator used. Simulation has been the primary tool for studying these statistics. Recently, Durbin obtained the distributions of D, D⁺ and D⁻ in terms of a Fourier transform for a wide class of underlying populations, and produced explicit…