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Learning Temporal Structures of Random Patterns by Generating Functions
The American Statistician ( IF 1.8 ) Pub Date : 2020-07-16 , DOI: 10.1080/00031305.2020.1778527
Yanlong Sun 1, 2, 3 , Hongbin Wang 3
Affiliation  

Abstract

We present a method of generating functions to compute the distributions of the first-arrival and inter-arrival times of random patterns in independent Bernoulli trials and first-order Markov trials. We use segmentation of pattern events and diagrams of Markov chains to illustrate the recursive structures represented by generating functions. We then relate the results of pattern time to the probability of first occurrence and the probability of occurrence at least once within a finite sample size. Through symbolic manipulation of formal power series and multiple levels of compression, generating functions provide a powerful way to discover the rich statistical structures embedded in random sequences.



中文翻译:

通过生成函数学习随机模式的时间结构

摘要

我们提出了一种生成函数的方法来计算独立伯努利试验和一阶马尔可夫试验中随机模式的首次到达时间和到达间隔时间的分布。我们使用模式事件的分段和马尔可夫链图来说明由生成函数表示的递归结构。然后我们将模式时间的结果与第一次出现的概率和在有限样本大小内至少出现一次的概率相关联。通过对形式幂级数和多级压缩的符号操作,生成函数提供了一种强大的方法来发现嵌入在随机序列中的丰富的统计结构。

更新日期:2020-07-16
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