Distribution of Patterns of Constrained Length in Binary Sequences

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 ana...

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Bibliographic Details
Published inMethodology and computing in applied probability Vol. 25; no. 4; p. 90
Main Authors Makri, Frosso S., Psillakis, Zaharias M.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2023
Springer Nature B.V
Subjects
Business and Management
Codes
Combinatorial analysis
Constraints
Economics
Electrical Engineering
Hypothesis testing
Information theory
Life Sciences
Mathematical analysis
Mathematics and Statistics
Random variables
Statistics
Constrained binary patterns and codes
60C05
Exact distributions
60G09
Exchangeable trials
62E12
Independent and identical trials
Combinatorial analysis
Runs
60E05
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-023-10068-5