Technical Abstract: For decades stochastic modelers have used computerized random number generators to produce random numeric sequences fitting a specified statistical distribution. Unfortunately, none of the random number generators we tested satisfactorily produced the target distribution. The result is generated distributions whose mean even diverges from the mean used to generate them, regardless of the length of run. Non-uniform distributions from short sequences of random numbers are a major problem in stochastic climate generation because truly uniform distributions are required to produce the intended climate parameter distributions. In order to ensure generation of a representative climate with the stochastic weather generator CLIGEN within a 30 year run, we tested the climate output resulting from various random number generators. The resulting distributions of climate parameters showed significant departures from the target distributions in all cases. We traced this failure back to the uniform random number generators themselves. This paper proposes a quality control approach to select only those numbers that conform to the expected distribution being retained for subsequent use. The approach is based on goodness of fit analysis applied to the generated random numbers. Normally-distributed deviates are further tested with confidence interval tests on their means and standard deviations. The positive effect of the new approach on the generated climate characteristics and subsequent deterministic process-based hydrology and soil erosion modeling are illustrated for four climatologically diverse sites.