脆弱性分布及其近似
Fragility Distributions and their approximations
摘要：
给定具有公共分布$F$的$n$同分布随机变量的序列，由$\FD$表示的\emph{fragility distribution of order $m$}是给定至少存在$m$一致性的一致性的数量的极限条件分布，因为阈值趋向于$F$的右端点。本文讨论了当$n$变大时，$\FD$的存在性及其渐近行为.对于平稳序列，当其随机过程收敛于复合泊松过程时，我们导出了计算$\lim_{n \to \infty} \FD$的显式公式。我们还建立了Stein的方法来估计脆弱性分布近似的误差。
英文摘要：
Given a sequence of $n$ identically distributed random variables with common distribution $F$, the \emph{fragility distribution of order $m$}, represented by $\FD$, is the limit conditional distribution of the number of exceedances given there are at least $m$ exceedances, as the threshold tends to the right end point of $F$. In this paper we are concerned with the existence of $\FD$ and its asymptotic behaviour when $n$ becomes large. For a stationary sequence with its exceedance process converging to a compound Poisson process, we derive an explicit formula for calculating $\lim_{n \to \infty} \FD$. We also establish Stein's method for estimating the errors involved in fragility distribution approximations.
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