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A model capable of changing the heaviness of the tail of a probability distribution function

Abstract Exceptional events may be declared exceptional due to underestimation of extreme values. We focus on the uncertainties associated with the transformation of extreme variables by a rainfall–runoff model, or by a catchment. Conditional probabilities provide a simple model that accounts for the modification of the extreme value index due to the rainfall–runoff transformation. In its original form, this model can only decrease the value of this index, but a modified form yields a family of distributions resilient to exponentially distributed perturbations, not subject to this restriction. The behaviour of these distributions in extreme values is related to the intensity of the perturbation versus the intensity of the relationship with the independent variable (rainfall). The tails of the rainfall and runoff distributions are not necessarily parallel. A case study is presented with positive – but not very different – values of the extreme value indexes. Complementary investigations are performed on synthetic data. As the model exhibits the same behaviour as a more detailed model, the transformation of the extreme value index clearly depends on the transfer function. Hydrological or hydraulic knowledge is therefore necessary to improve estimation of the upper tail of flood distributions. Citation Leviandier, T. (2010) A model capable of changing the heaviness of the tail of a probability distribution function. Hydrol. Sci. J. 55(6), 992–1001.