While lognormal distributions have been proposed as useful descriptors of recruitment variability, the very nature of the recruitment distributions is still debated. To account quantitatively for recruitment distributions, I here propose a Weibull exponential model; it derives from a simple and natural hypothesis for uncorrelated recruitment processes of spawning, hatching, growth and survival through the early life stages to the point of vulnerability to the fishery. The quantification of Weibull exponentials is particularly important with regards to extrapolations to low recruits that have not yet been observed. To test the Weibull exponential null-hypothesis, I examine annual time-series of recruitment in major aquatic stocks. The Weibull exponential quite describes the bulk (95%) of the recruitment distributions of widely differing stocks, while the remaining 5% of the largest recruits are occurring with a much larger rate than predicted by the Weibull exponential. Further, I study the inter-event times between unusually high numbers in recruitment time-series data and find that intermittent pulses of strong recruitment follow non-Poisson statistics, which arises from year-to-year persistence of the magnitude of recruitment: large (or small) recruits are more likely to be followed by large (or small) recruits. This recruitment clustering effect is confirmed by the rescaled range analysis method. The empirical results imply that individual survivals on recruitment levels are independent of initial cohort sizes but year-to-year recruiting events exhibit long-term correlations.