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Record Statistics from Point Process Models

In: Extreme Value Theory and Applications

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  • H. N. Nagaraja

    (The Ohio State University)

Abstract

Let X0, X1,… be a sequence of independent identically distributed random variables with a continuous distribution function. Suppose these are observed at successive time points determined by an independent point process P defined on positive reals. We say Xj is an upper record value if Xj = max(X0,…, Xj). Let {RjS, j ≥ 1} be the sequence of upper records and let {Tj, j ≥ 1} be the times at which these records are observed. We describe the distribution of these and related record statistics under various assumptions on P. We discuss some applications of the results to climatology, shock models, and the best-choice problem.

Suggested Citation

  • H. N. Nagaraja, 1994. "Record Statistics from Point Process Models," Springer Books, in: Janos Galambos & James Lechner & Emil Simiu (ed.), Extreme Value Theory and Applications, pages 355-370, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3638-9_21
    DOI: 10.1007/978-1-4613-3638-9_21
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