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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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