A limit theorem for the number of non-overlapping occurrences of a pattern in a sequence of independent trials
- 1 June 1988
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 25 (2) , 428-431
- https://doi.org/10.2307/3214452
Abstract
A sequence of independent experiments is performed, each producing a letter from a given alphabet. Using a result by Barbour and Eagleson (1984) we prove that under general conditions the number of non-overlapping occurrences of long recurrent patterns has approximately a Poisson distribution.Keywords
This publication has 20 references indexed in Scilit:
- Run probabilities and the motion of a particle on a given pathJournal of Applied Probability, 1986
- Renewal theory for several patternsJournal of Applied Probability, 1985
- The occurrence of sequence patterns in ergodic Markov chainsStochastic Processes and their Applications, 1984
- Poisson approximation for some statistics based on exchangeable trialsAdvances in Applied Probability, 1983
- How many random digits are required until given sequences are obtained?Journal of Applied Probability, 1982
- On the mean number of random digits until a given sequence occursJournal of Applied Probability, 1982
- String overlaps, pattern matching, and nontransitive gamesJournal of Combinatorial Theory, Series A, 1981
- Periods in stringsJournal of Combinatorial Theory, Series A, 1981
- The limit distribution of the length of the longest head-runPeriodica Mathematica Hungarica, 1979
- Success runs in a two-state Markov chainJournal of Applied Probability, 1974