Distributions of Patterns of Pair of Successes Separated by Failure Runs of Length at Least k_1 and at Most k_2 Involving Markov Dependent Trials: GERT Approach

Kanwar Sen; Pooja Mohan; Manju Lata Agarwal

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Distributions of Patterns of Pair of Successes Separated by Failure Runs of Length at Least k_1 and at Most k_2 Involving Markov Dependent Trials: GERT Approach

机译：涉及马尔科夫相关试验的最少k_1和最大k_2的，由长度失败的行程分开的成对成功模式的分布：GERT方法

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We use the Graphical Evaluation and Review Technique (GERT) to obtain probability generating functions of the waiting time distributions of 1st, and mth nonoverlapping and overlapping occurrences of the pattern Λ_f~(k_1,k_2) = SFF···FS/k_1≤k_f≤k_2(k_1 ＞ 0), involving homogenous Markov dependent trials. GERT besides providing visual picture of the system helps to analyze the system in a less inductive manner. Mean and variance of the waiting times of the occurrence of the patterns have also been obtained. Some earlier results existing in literature have been shown to be particular cases of these results.

机译：我们使用图形评估和审查技术（GERT）获得第1次等待时间分布的概率生成函数，以及第m次非重叠和重叠出现的模式Λ_f〜（k_1，k_2）= SFF···FS /k_1≤k_f ≤k_2（k_1＞ 0），涉及同质的马尔可夫依赖试验。 GERT除了提供系统的可视图片之外，还有助于以更少的归纳方式分析系统。还获得了图案出现的等待时间的平均值和方差。文献中已有的一些较早的结果已证明是这些结果的特殊情况。

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《International journal of quality, statistics, & reliability》 |2013年第2013期|494976.1-494976.9|共9页
作者
Kanwar Sen; Pooja Mohan; Manju Lata Agarwal;
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Department of Statistics, University of Delhi, Delhi 7, India;

RMS India, A-7, Sector 16, Noida 201 301, India;

The Institute for Innovation and Inventions with Mathematics and IT (IIIMIT),Shiv Nadar University, Greater Noida 203207, India;

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1. Distributions of Patterns of Pair of Successes Separated by Failure Runs of Length at Leastk1and at Mostk2Involving Markov Dependent Trials: GERT Approach [J] . KanwarSen, PoojaMohan, Manju LataAgarwal Journal of Quality and Reliability Engineering . 2013,第4期

机译：涉及马尔可夫相关试验的在Leastk1和Mostk2上由长度失败的行程分开的成对成功模式的分布：GERT方法
2. Distributions associated with (k_1,k_2) events on semi-Markov binary trials [J] . Stefanov V.T., Manca R. Journal of Statistical Planning and Inference . 2013,第7期

机译：半马尔可夫二元试验中与（k_1，k_2）事件相关的分布
3. The Exact and Limiting Distributions for the Number of Successes in Success Runs Within a Sequence of Markov-Dependent Two-State Trials [J] . James C. Fu, W. Y. Wendy Lou, Zhi-Dong Bai, Annals of the Institute of Statistical Mathematics . 2002,第4期

机译：在一系列依赖于马尔科夫的二态试验中，成功运行的成功次数的精确和极限分布
4. Waiting Time Distributions of Patterns Involving Homogenous Markov Dependent Trials: GERT Approach [C] . POOJA MOHAN, KANWAR SEN, MANJU LATA AGARWAL Proceedings of the 7th international conference on "mathematical methods in reliability": theory, methods, applications. . 2011

机译：涉及均质马尔可夫依赖试验的模式的等待时间分布：GERT方法
5. Representing context-dependent categorical and mixed-value data systems for fault and anomaly detection: A highly scalable variable length Markov approach. [D] . Brice, Pierre. 2009

机译：表示用于故障和异常检测的上下文相关分类和混合值数据系统：一种高度可扩展的可变长度Markov方法。
6. A data-driven approach to predicting successes and failures of clinical trials [O] . Kaitlyn Gayvert, Neel Madhukar, Olivier Elemento -1

机译：一种数据驱动的方法来预测临床试验的成功和失败
7. Generalizations of distributions related to ( $$k_1,k_2$$ k 1 , k 2 )-runs [O] . A. N. Kumar, N. S. Upadhye 2018

机译：与（$$ k_1，k_2 $$ k 1，k 2）-runs相关的分布概括

Distributions of Patterns of Pair of Successes Separated by Failure Runs of Length at Least k_1 and at Most k_2 Involving Markov Dependent Trials: GERT Approach

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