Generation of quasi-random numbers with exact statistics

System models are generally developed for predicting the outcome of the system under test due to a preset input. This is true not only for problems in mathematics, physics and engineering but also for problems in economics, medicine and social sciences. System models should involve random variables if the system knowledge is not deterministic. In this paper, the method of uniform sampling (MUS) is proposed for the generation of statistically very accurate numbers for an arbitrary distribution. MUS is illustrated for uniform and standard normal distributions. Its performance is tested using quantitative `quality´ measures. A practical algorithm for the generation of a statistically very accurate samples for an arbitrary distribution is given. the generated number and the generator itself are tested to be very accurate using the quality measure.