The late Jan van Noortwijk (JvN) made valuable contributions in many areas such as Reliability, Risk management, Maintenance modelling, Applications to Decision theory and more. His contributions to model river discharges for flood prevention (van Noortwijk et al., [1, 2] and others) are of interest to forecast river stream flow. The posterior predictive densities for several distributions, which can be considered as candidates to model river discharges, were derived using Jeffreys prior. The Jeffreys prior was derived for these distributions by careful algebraic derivations of the Fisher information matrix. The posterior predictive density is the way we believe to follow for predicting future values once the best model is selected. Van Noortwijk et al. [1, 2] proposed Bayes weights for selecting the best model. The advantage of the posterior predictions over substituting the estimates of the parameters in the quantile function is discussed for a special case. A further application under regression in the lognormal model with the Southern Oscillation Index (SOI) as independent variable, is shown for the annual discharge of the Orange River in South Africa. It implies the prediction of the SOI at least one year ahead through an autoregressive time series.