Record Statistics from Point Process Models

H. N. Nagaraja
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H. N. Nagaraja: The Ohio State University

A chapter in Extreme Value Theory and Applications, 1994, pp 355-370 from Springer

Abstract: 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.

Keywords: Point Process; Homogeneous Poisson Process; Continuous Distribution Function; Point Process Model; Extremal Process (search for similar items in EconPapers)
Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-3638-9_21

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DOI: 10.1007/978-1-4613-3638-9_21

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