{"title":"Distribution of Patterns of Constrained Length in Binary Sequences","authors":"Frosso S. Makri, Zaharias M. Psillakis","doi":"10.1007/s11009-023-10068-5","DOIUrl":null,"url":null,"abstract":"<p>On a finite sequence of binary (0-1) trials we define a random variable enumerating patterns of length subject to certain constraints. For sequences of independent and identically distributed binary trials exact probability mass functions are established in closed forms by means of combinatorial analysis. An explicit expression of the mean value of this random variable is obtained. The results associated with the probability mass functions are extended on sequences of exchangeable binary trials. An application in Information theory concerning counting of a class of run-length-limited binary sequences is provided as a direct byproduct of our study. Illustrative numerical examples exemplify further the results.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":"36 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methodology and Computing in Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11009-023-10068-5","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
On a finite sequence of binary (0-1) trials we define a random variable enumerating patterns of length subject to certain constraints. For sequences of independent and identically distributed binary trials exact probability mass functions are established in closed forms by means of combinatorial analysis. An explicit expression of the mean value of this random variable is obtained. The results associated with the probability mass functions are extended on sequences of exchangeable binary trials. An application in Information theory concerning counting of a class of run-length-limited binary sequences is provided as a direct byproduct of our study. Illustrative numerical examples exemplify further the results.
期刊介绍：
Methodology and Computing in Applied Probability will publish high quality research and review articles in the areas of applied probability that emphasize methodology and computing. Of special interest are articles in important areas of applications that include detailed case studies. Applied probability is a broad research area that is of interest to many scientists in diverse disciplines including: anthropology, biology, communication theory, economics, epidemiology, finance, linguistics, meteorology, operations research, psychology, quality control, reliability theory, sociology and statistics.
The following alphabetical listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interests:
-Algorithms-
Approximations-
Asymptotic Approximations & Expansions-
Combinatorial & Geometric Probability-
Communication Networks-
Extreme Value Theory-
Finance-
Image Analysis-
Inequalities-
Information Theory-
Mathematical Physics-
Molecular Biology-
Monte Carlo Methods-
Order Statistics-
Queuing Theory-
Reliability Theory-
Stochastic Processes
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