Mathematical models have been developed that can completely describe the distribution of sediment concentration from the channel bed to the water surface. These models can be used to estimate the mean (depth-averaged) sediment concentration by a quick, point sampling in river engineering practice. The developed models are products of a combined application of the deterministic and probabilistic concepts. The complementary nature of the two concepts strengthens the methodology of describing the various features of sediment transport. The models incorporate a velocity distribution equation that corresponds to a probability distribution derived by maximizing the information entropy. The probability distribution is a compact description of the system at a channel section, and its resilience or stability explains the applicability of the developed models of velocity and sediment distributions in a wide range of flows, steady or unsteady.