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Abstract In previous studies, beta-k distribution and distribution functions strongly related to that, have played important roles in representing extreme events. Among these distributions, the Beta-Singh-Maddala turned out to be adequate for modelling hydrological extreme events. Starting from this distribution, the aim of the paper is to express the model as a function of indexes of hydrological interest and simultaneously investigate on their dependence with a set of explanatory variables in such a way to explore on possible determinants of extreme hydrologic events. Finally, an application to a real hydrologic dataset is considered in order to show the potentiality of the proposed model in describing data and in understanding effects of covariates on frequently adopted hydrological indicators.