Detecting changes in probabilities of a multi—component process
Detecting changes in probabilities of a multi—component process
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检测多组件过程的概率变化
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
R. Khan
中科院分区：
文献类型：
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作者：
R. Khan
设n = 1，n = 2，.定义cusum（累积和）停止时间，其中h是正整数。当（a）q > p（指数）和（B）p = q时，我们得到了N1（h）的适当归一化函数的渐近（当h → ∞）分布.作为一个应用，我们定义了一个cusum过程检测的概率变化的多分量过程，并使用（a），我们得到的平均游程长度（ARL）的给定程序的渐近近似。在适当的条件下，推广了上述关于任意iid随机变量序列X1，X2，…，μ≤0的渐近结果.
Let ξ1,ξ2,… be iid random variables such that P(ξ1 = 1) = p, [ILM001] and set S0 = 0, Sn, = ξ1+…+ξn, n ≥ 1. Define the cusum (cumulative sum) stopping time , where h is a positive integer. We find asymptotic (as h → ∞) distributions of suitably normalized functions of N1(h) when (a)q > p (exponential) and (b) p = q. As an application we define a cusum procedure for detecting changes in probabilities of a multi—component process, and using (a) we obtain an asymptotic approximation for the average run length (ARL) of the given procedure. Moreover, under some suitable conditions we generalize the preceding asymptotic results for any sequence of iid random variables X1, X2,… with mean μ≤0.