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1 results

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

  • Dariush Haghighi-Talab, Christopher Wright
  • Journal:
    Journal of Applied Probability / Volume 10 / Issue 3 / September 1973
    Published online by Cambridge University Press:
    14 July 2016, pp. 556-571
    Print publication:
    September 1973

  • 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.