Abstract
Let {Xn
, n ≧ 1} be i.i.d. and Yn
= max {X
1,…, Xn
}. Xj
is a record value of {Xn
} if Yj > Yj–
1 The record value times are Ln, n ≧ 1 and inter-record times are Δ
n
, n ≧ 1. The known limiting behavior of {Ln
} and {Δn
} is close to that of a non-homogeneous Poisson process and an explanation of this is obtained by embedding {Yn
} in a suitable extremal process which jumps according to a non-homogeneous Poisson process.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
11 articles.
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1. Extremal Processes;Wiley StatsRef: Statistics Reference Online;2014-09-29
2. Extremal processes, secretary problems and the 1/e law;Journal of Applied Probability;1989-12
3. Records in the presence of a linear trend;Advances in Applied Probability;1987-12
4. Records in the presence of a linear trend;Advances in Applied Probability;1987-12
5. On a joint strong approximation theorem for record and inter-record times;Probability Theory and Related Fields;1987-06