Statistical Inference for Discrete Patterns

离散模式的统计推断

基本信息

批准号：
11640116
负责人：
AKI Sigeo
金额：
$ 1.15万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640116/
关键词：
discrete patterns discrete distribution theory directed tree probability generating function Markov chain system reliability binomial distribution waiting time problems 離散分布パターン連工学的システム信頼性経験分布関数

项目摘要

We have studied waiting time distributions of runs and patterns in random structures such as sequences of random variables and random directed trees. The following results are derived.1. We have obtained the exact distribution of the number of "1" -runs of a specified length on {0, 1} -valued Markov trees. This result can be applied to calculate the reliability of a consecutive system on a directed tree. We also obtained the exact distribution of the life time of the consecutive system on the directed tree.2. We have studied exact distributions of sooner and later waiting times for runs in Markov dependent bivariate trials. We have given systems of linear equations with respect to conditional probability generating functions of the waiting times and have solved them. This result can be applied to calculate the reliability of the linear connected- (r, s) -out-of- (r+1, n) : F lattice system.3. We have introduced a Markov chain imbeddable vector of multinomial type and a Markov chain imbeddable variables of returnable type and have discussed some of their properties. By using the result we have derived the distribution of numbers of occurrences of runs of specified lengths in a sequence of multi-state trials.4. We have introduced a unified counting scheme for runs called 1-overlapping counting. We have given exact probability generating function of the number of 1-overlapping 1-runs of a specified length in some dependent random sequences such as a Markov chain and a heigher order Markov chain.5. We have introduced a new type of dependent sequence called a binary sequence of order (k, r) and have derived the exact distributions of sooner and later waiting times for success and failure runs in the sequence.

我们研究了在随机结构中的等待时间分布，例如随机变量的序列和随机有向树的序列。得出以下结果1。我们已经获得了{0，1}估计的马尔可夫树上指定长度的“ 1”额数的确切分布。可以应用此结果来计算有向树上连续系统的可靠性。我们还获得了连续系统在定向树上的寿命的确切分布。2。我们已经研究了在马尔可夫依赖的双变量试验中的早期和晚期等待时间的精确分布。我们为等待时间的有条件概率生成函数并解决了线性方程的系统。可以应用此结果来计算线性连接的可靠性 - （r，s）-out-of-（r+1，n）：f lattice System.3。我们已经引入了Markov链嵌入的多项式类型的可嵌入矢量和Markov链嵌入式可返回类型的变量，并讨论了它们的某些属性。通过使用结果，我们得出了以多状态试验为单位的指定长度运行数量的分布。4。我们已经引入了一种统一计数方案，用于称为1跨拼接计数的运行。我们给出了在某些相关随机序列（例如马尔可夫链和较高的秩序马尔可夫链）中，指定长度的1重叠1跑数的数量的确切概率生成函数。5。我们引入了一种称为二进制序列（K，R）二进制序列的新类型的依赖序列，并得出了以序列成功和失败运行的早期和较晚的等待时间的精确分布。