It has been known for a long time that sediment transport rates can vary strongly even if the ambient hydraulic conditions remain steady. In this article, a new approach is described to derive probability distributions of bed load transport rates, starting from the waiting time between the arrivals of individual sediment particles. The formalism should be valid when transport is not dominated by bed form motion. Without any assumptions about the distribution of interarrival times, the approach yields the Birnbaum-Saunders distribution, a two-parameter distribution previously used in lifetime modeling. Observed dependence of mean transport rates on the sampling time and multiscaling are predicted by the distribution. Assuming exponentially and Poisson-distributed interarrival times, the same approach yields the Poisson and the gamma distributions. Using a high-resolution bed load transport data set from the Pitzbach, Austria, the distribution functions are tested on field data. The gamma distribution best describes the data, with maximum deviations of similar to 5%. However, the Birnbaum-Saunders distribution may be more useful in certain applications, as it is a general approximation in the proposed formalism and no debated assumptions are necessary for its derivation.