Multivariate quantiles in hydrological frequency analysis
Article first published online: 11 SEP 2009
Copyright © 2009 John Wiley & Sons, Ltd.
Volume 22, Issue 1, pages 63–78, February 2011
How to Cite
Chebana, F. and Ouarda, T.B.M.J. (2011), Multivariate quantiles in hydrological frequency analysis. Environmetrics, 22: 63–78. doi: 10.1002/env.1027
- Issue published online: 11 SEP 2009
- Article first published online: 11 SEP 2009
- Manuscript Accepted: 4 AUG 2009
- Manuscript Received: 24 NOV 2008
- Natural Sciences and Engineering Research Council (NSERC)
- Canada Research Chair Program
- frequency analysis;
- multivariate quantile;
Several hydrological phenomena are described by two or more correlated characteristics. These dependent characteristics should be considered jointly to be more representative of the multivariate nature of the phenomenon. Consequently, probabilities of occurrence cannot be estimated on the basis of univariate frequency analysis (FA). The quantile, representing the value of the variable(s) corresponding to a given risk, is one of the most important notions in FA. The estimation of multivariate quantiles has not been specifically treated in the hydrological FA literature. In the present paper, we present a new and general framework for local FA based on a multivariate quantile version. The multivariate quantile offers several combinations of the variable values that lead to the same risk. A simulation study is carried out to evaluate the performance of the proposed estimation procedure and a case study is conducted. Results show that the bivariate estimation procedure has an analogous behaviour to the univariate one with respect to the risk and the sample size. However, the dependence structure between variables is ignored in the univariate case. The univariate estimates are obtained as special combinations by the multivariate procedure and with equivalent accuracy. Copyright © 2009 John Wiley & Sons, Ltd.