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2 results

  • On the number and sum of near-record observations

  • Part of
  • N. Balakrishnan, A.G. Pakes, A. Stepanov
  • Journal:
    Advances in Applied Probability / Volume 37 / Issue 3 / September 2005
    Published online by Cambridge University Press:
    01 July 2016, pp. 765-780
    Print publication:
    September 2005
    • Article
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  • Let X1,X2,… be a sequence of independent and identically distributed random variables with some continuous distribution function F. Let L(n) and X(n) denote the nth record time and the nth record value, respectively. We refer to the variables Xi as near-nth-record observations if Xi∈(X(n)-a,X(n)], with a>0, and L(n)<i<L(n+1). In this work we study asymptotic properties of the number of near-record observations. We also discuss sums of near-record observations.

  • On record values and record times

  • R. W. Shorrock
  • Journal:
    Journal of Applied Probability / Volume 9 / Issue 2 / June 1972
    Published online by Cambridge University Press:
    14 July 2016, pp. 316-326
    Print publication:
    June 1972

  • A correspondence between record values and independent increment point processes is established. The asymptotic behaviour of record value sequences is studied, and results on the asymptotic behaviour of record times (for continuous F) are obtained as special cases. The joint law of the kth record value and the kth record time is also derived.