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Runs on a circle

Part of: Markov processes Limit theorems Distribution theory

Published online by Cambridge University Press:  14 July 2016

M. V. Koutras ,
G. K. Papadopoulos  and
S. G. Papastavridis
M. V. Koutras*
Affiliation:
University of Athens
G. K. Papadopoulos*
Affiliation:
University of Athens
S. G. Papastavridis*
Affiliation:
University of Athens
*
∗Postal address for all authors: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece.
∗Postal address for all authors: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece.
∗Postal address for all authors: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece.
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Abstract

In the present paper we study the number of occurrences of non-overlapping success runs of length in a sequence of (not necessarily identical) Bernoulli trials arranged on a circle. An exact formula is given for the probability function, along with some sharp bounds which turn out to be very useful in establishing limiting (Poisson convergence) results. Certain applications to statistical run tests and reliability theory are also discussed.

Keywords

CIRCULAR SUCCESS RUNSBERNOULLI TRIALSMARKOV CHAINSCHEN–STEIN METHODPOISSON CONVERGENCEBINOMIAL DISTRIBUTIONS OF ORDER k

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 62E15: Exact distribution theory 62E17: Approximations to distributions (nonasymptotic) 60F99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 396 - 404
Copyright
Copyright © Applied Probability Trust 1995 

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