论文标题
生存数据中的极端和未经审查的寿命
Extremes of Censored and Uncensored Lifetimes in Survival Data
论文作者
论文摘要
I.I.D.生存分析的审查模型假定I.I.D的两个独立序列。正随机变量，$（t_i^*）_ {1 \ le i \ le n} $和$（u_i）_ {1 \ le i \ le n} $。数据包括对随机顺序$ \ big的观察（t_i = \ min（t_i^*，u_i）$以及随附的审查指标。$ t_i $带有$ t_i^*\ le u_i $的值，据说是未经经过审查的，这些$ t_i^*> u_i $ and $ the $ the $ the $ the $ the $ the $ the $ the $ the us the us pabe us the us the us the us the us the us the us the us pabe use us the us pabe。 Gumbel分布的吸引力和渐近分布作为样本大小$ n \ to \ infty $，是数据中审查和未经审查的寿命的最大值，以及与之相关的统计数据。
The i.i.d. censoring model for survival analysis assumes two independent sequences of i.i.d. positive random variables, $(T_i^*)_{1\le i\le n}$ and $(U_i)_{1\le i\le n}$. The data consists of observations on the random sequence $\big(T_i=\min(T_i^*,U_i)$ together with accompanying censor indicators. Values of $T_i$ with $T_i^*\le U_i$ are said to be uncensored, those with $T_i^*> U_i$ are censored. We assume that the distributions of the $T_i^*$ and $U_i$ are in the domain of attraction of the Gumbel distribution and obtain the asymptotic distributions, as sample size $n\to\infty$, of the maximum values of the censored and uncensored lifetimes in the data, and of statistics related to them. These enable us to examine questions concerning the possible existence of cured individuals in the population.
