Risk Assessment Using A Generalized Pareto-based Bivariate Model
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F. Ashkar & N. El-Jabi
Risk assessment using a generalized Pareto- based bivariate model F. Ashkar1 & N. El-Jabi2 1 Department of Mathematics and Statistics, Universite de Moncton, Canada. 2 Faculty of Engineering, Universite de Moncton, Canada. Abstract In hydrology, one often has to study the joint probabilistic behavior of two or more variables characterizing a water system. A model constructed from generalized-Pareto-distributed (GPD) marginals is presented in the present paper to study the relation between two variables. The GPD model is the most popular one used in the 'Peaks-Over-Threshold' (POT) approach for studying hydrological extremes, and is also applicable in the 'Deficit-Below-Threshold' (DBT) approach for modeling low extremes. The bivariate model presented herein, allows for risk assessments and calculations associated with each hydrological variable separately, with one variable conditioned by the other, or with both variables taken together. It will be used to model the joint distribution of the duration (X1 and the peak discharge above a threshold (X2 of a real flood series derived from hydrometric data of the Little Southwest Miramichi River, in New Brunswick, Canada. 1 Introduction In hydrology, one must often consider water systems where several random variables act individually or jointly on the system. For example, one must simultaneously take into account the intensity, duration and frequency of precipitation events when studying urban drainage systems. Likewise, the duration as well as the volume of low flows must be taken into account in managing water reservoirs, or in irrigation. It is important to be able to adequately describe the joint probability laws that govern the variables acting within the system.