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Two extreme value processes arising in hydrology

Published online by Cambridge University Press:  14 July 2016

Alan F. Karr
Alan F. Karr*
Affiliation:
The Johns Hopkins University
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Abstract

Let Tn be the time of occurrence of the nth flood peak in a hydrological system and Xn the amount by which the peak exceeds a base level. We assume that ((Tn, Xn)) is a Poisson random measure with mean measure μ(dx) K(x, dy). In this note we characterize two extreme value processes which are functionals of ((Tn, Xn)). The set-parameterized process {MA} defined by MA = sup {Xn:Tn ∈ A} is additive and we compute its one-dimensional distributions explicitly. The process (Mt), where Mt = sup{Xn: Tn ≦ t}, is a non-homogeneous strong Markov process. Our results extend but computationally simplify those of previous models.

Keywords

HYDROLOGYFLOOD PEAKPOISSON RANDOM MEASUREEXTREME VALUE PROCESSSTRONG MARKOV PROPERTY
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 190 - 194
Copyright
Copyright © Applied Probability Trust 1976 

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References

Çinlar, E. (1971) Random measures and dynamic point processes. Unpublished lecture notes, Northwestern University.Google Scholar
Todorovic, P. (1970) On some problems involving random number of random variables. Ann. Math. Statist. 41, 1059–1063.CrossRefGoogle Scholar
Zelenhasic, E. (1970) Theoretical probability distributions for flood peaks. Colorado State University Hydrology Papers, No. 42, Colorado State University, Fort Collins, Colorado.Google Scholar