Exact Determination of the Run Length Distribution of a One-Sided CUSUM Procedure Applied on an Ordinary Poisson Process

S. Zacks

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Exact Determination of the Run Length Distribution of a One-Sided CUSUM Procedure Applied on an Ordinary Poisson Process

机译：精确确定普通Poisson过程中单面CUSUM程序的游程长度分布

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The structure of a CUSUM procedure on an ordinary Poisson jump process is analyzed in terms of stopping rules based on linear boundaries. The total run length is composed of a random number of renewal phases followed by a terminal phase. The exact distributions of the length of these phases are derived, as well as the Wald type approximations. The distribution of the total run length and its moments is given in terms of the phase distributions.

机译：根据基于线性边界的停止规则，分析了普通Poisson跳跃过程中CUSUM过程的结构。总运行时间由随机数的续订阶段和随后的终止阶段组成。得出这些相的长度的确切分布以及Wald型近似。总运行长度及其力矩的分布根据相位分布给出。

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来源
《Sequential analysis》 |2004年第2期|p.159-178|共20页
作者
S. Zacks;
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作者单位

Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USA;

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原文格式 PDF
正文语种 eng
中图分类统计学;
关键词
poisson process; cumulative sums control; detection of change points; distribution of run length; stopping times with linear boundaries;

机译：泊松过程;累积和控制;变化点的检测;行程的分布;线性边界的停止时间;

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2. Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes [J] . Hodjat Pendar, Thierry Platini, Rahul V. Kulkarni PHYSICAL REVIEW E . 2013,第4期

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3. Using CUSUM control schemes for monitoring quality levels in compound Poisson production environment: The geometric Poisson process [J] . Ching- Wen Chen, Palll H. Randolph, Tian-Shy Lioll Quality Control and Applied Statistics . 2007,第2期

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5. Exact methods applied to group sequential and other stratified comparative Poisson designs. [D] . Xia, Qi. 2005

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7. Determination of probability distributions for Strahler stream lengths based on Poisson process and DEM [O] . Ming-sang Yang, Kwan Tun Lee 2001

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8. A New Approach to the Determination of Exact and Approximate One-Sided Prediction Intervals for Normal and Lognormal Distributions,with Tables. [R] . fertig,kenneth w. mann,nancy r. 1974

机译：用表确定正态分布和对数正态分布的精确和近似单边预测区间的新方法。

Exact Determination of the Run Length Distribution of a One-Sided CUSUM Procedure Applied on an Ordinary Poisson Process

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