An application of the Bivariate Generalized Pareto Distribution for the probabilities of low flow extremes estimation

Abstract. The two-dimensional Bivariate Generalized Pareto Distribution (BGPD) of Tajvidi (1996) is applied in order to estimate the extreme values of the low flow deficit amounts and durations probabilities. Eight parameters BGPD depends on two one-dimensional distributions – Univariate Generalized Pareto Distributions (UGPDs). Each of these three parameter UGPDs describes the probability of one of low flow indices. To fit BGPD into observed data a three steps method of estimation is proposed: (1) For a given shift parameter of each UGPD two others are estimated by the maximum likelihood method. (2) For given shifts and the UGPD parameters estimated in the first step the remaining ones, connected to the bivariate distribution function formula, are also estimated by the maximum likelihood method. (3) The best shift pair is chosen by maximization of the correlation coefficient of the estimated BGPD. The results are applied to statistical description of the low flow index extremes behaviour at four different catchments profiles. To extract the low flow time series data the standard constant threshold level method is applied. Finally the estimated probabilities are compared to the Zelenhasic and Salvai (1987) model.