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On the distribution of records in a finite sequence of observations, with an application to a road traffic problem

Published online by Cambridge University Press:  14 July 2016

Dariush Haghighi-Talab  and
Christopher Wright
Dariush Haghighi-Talab
Affiliation:
University College, London
Christopher Wright
Affiliation:
University College, London
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Abstract

Probability distributions relating to the number and positions of lower records in a finite sequence of observations are obtained by methods involving the permutation of ranks. Some new results, and results of earlier authors, are expressed in a form thought to be useful for direct practical applications.

Expressions are also given for the distribution of the length of a ‘record run’, which consists of the observations following and including a given record either up to the next record, or, if a further record does not occur, up to the end of the sequence of observations. This quantity, whose distribution is closely related to that of the inter-record time, has a direct and simple application to road traffic leaving a signal which has been confirmed by experimental observation.

Keywords

RECORD VALUES IN FINITE SEQUENCESELEMENTARY FORMULAEROAD TRAFFIC LEAVING SIGNAL
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 556 - 571
Copyright
Copyright © Applied Probability Trust 1973 

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References

Abramowitz, M. and Segun, I. A., (Eds.) (1965) Handbook of Mathematical Functions. Dover, New York. 833 ff.Google Scholar
Barton, D. E. and Mallows, C.L. (1965) Some aspects of the random sequence. Ann. Math. Statist. 36, 236–260.Google Scholar
Chandler, K. N. (1952) The distribution and frequency of record values. J. Roy. Statist. Soc. B 14, 220–228.Google Scholar
David, F. N. and Barton, D. E. (1962) Combinatorial Chance. Griffin, London. 179 ff.Google Scholar
Foster, F. G. and Stuart, A. (1954) Distribution-free tests in time series based on the breaking of records. J. Roy. Statist. Soc. B 16, 1–22.Google Scholar
Kleinman, S. (1972) A mathematical model for platoon formation. Transportation Sc. 6, 2, 202–204.Google Scholar
Miksa, F. L. (1956) Stirling numbers of the first kind, (unpub.; see Review No.7 (I), Math. Tables and Other Aids to Computation 10, 37, (1956)).Google Scholar
Moser, L. and Wyman, M. (1958) Asymptotic development of the Stirling numbers of the first kind. J. London Math. Soc. 33, 133–146.10.1112/jlms/s1-33.2.133Google Scholar
Wright, C. C. (1970) Some characteristics of traffic leaving a signalised intersection. Transportation Sc. 4, 4, 331–346.Google Scholar