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

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 applica...

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Bibliographic Details
Published in:Journal of applied probability 1973-09, Vol.10 (3), p.556-571
Main Authors: Haghighi-Talab, Dariush, Wright, Christopher
Format: Article
Language:English
Subjects:
Mathematical sequences
Motor vehicle traffic
Probability distributions
Research Papers
Road medians
Roads
Speed
Statistical median
Traffic lights
Traffic models
Vehicles
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Summary: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.
ISSN:0021-9002
1475-6072
DOI:10.2307/3212776