The quantification of stream flow in ungauged basins is one of the most challenging tasks in surface water hydrology due to non-availability of data and system heterogeneity. Even though physics based distributed hydrologic models are considered best suited for the ungauged basins, uncertainty in model simulations, in the absence of any parameter estimations reflecting accurate watershed characteristics, may be high. A successful application of these models in making hydrologic response predictions in ungauged basins requires reducing number of parameters and output uncertainty. The current study proposes a method to minimize the predictive uncertainty of distributed hydrological models by deriving regionalized probability distribution of sensitive parameters of the model. To facilitate stochastic validation of the model in ungauged basins, the derived PDF of the parameters are obtained for a number of gauged basins, the derived PDFs are regionalized and then transferred to the ungauged basin. The method is illustrated through a case study of SWAT model applied to a watershed.