Open Access
December 2015 Extremes on river networks
Peiman Asadi, Anthony C. Davison, Sebastian Engelke
Ann. Appl. Stat. 9(4): 2023-2050 (December 2015). DOI: 10.1214/15-AOAS863


Max-stable processes are the natural extension of the classical extreme-value distributions to the functional setting, and they are increasingly widely used to estimate probabilities of complex extreme events. In this paper we broaden them from the usual situation in which dependence varies according to functions of Euclidean distance to situations in which extreme river discharges at two locations on a river network may be dependent because the locations are flow-connected or because of common meteorological events. In the former case dependence depends on river distance, and in the second it depends on the hydrological distance between the locations, either of which may be very different from their Euclidean distance. Inference for the model parameters is performed using a multivariate threshold likelihood, which is shown by simulation to work well. The ideas are illustrated with data from the upper Danube basin.


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Peiman Asadi. Anthony C. Davison. Sebastian Engelke. "Extremes on river networks." Ann. Appl. Stat. 9 (4) 2023 - 2050, December 2015.


Received: 1 February 2015; Revised: 1 July 2015; Published: December 2015
First available in Project Euclid: 28 January 2016

zbMATH: 06560819
MathSciNet: MR3456363
Digital Object Identifier: 10.1214/15-AOAS863

Keywords: extremal coefficient , hydrological distance , Max-stable process , network dependence , threshold-based inference , upper Danube basin

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.9 • No. 4 • December 2015
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