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一致随机序约束下的生存曲线估计AI 解读

If F and G are cumulative distribution functions on [0, ∞) governing the lifetimes of specific systems under study, and if F and G are their corresponding survival functions, then F is said to be uniformly stochastically smaller than G, denoted by F <(+) G, if and only if the ratio l(x) = G (x)/ F (x) is nondecreasing for x ∈ [0, sup{t: [0, sup {(t: F (t) > 0}). When F and G are absolutely continuous, F (+) G is equivalent to the assumption that the corresponding failure…

基于分位数函数比值的纯尾部排序AI 解读

In the intuitive approach, a distribution function $F$ is said to be not more heavily tailed than $G$ if $\lim \sup_{x \rightarrow \infty} \bar{F}/\bar{G} < \infty$. An alternative is to consider the behavior of the ratio $F^{-1}(u)/G^{-1}(u)$, in a neighborhood of one. The present paper examines the relationship between these two criteria and concludes that the intuitive approach gives a more thorough comparison of distribution functions than the ratio of the quantile…