Risk assessment using a generalized Pareto-based bivariate model

摘要

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 (X_1 and the peak discharge above a threshold (X_2) of a real flood series derived from hydrometric data of the Little Southwest Miramichi River, in New Brunswick, Canada.