Arbitrary numerical distributions are presented for use in devices having limited processing and storage capabilities by having the device accept strings of arbitrarily distributed numbers from a source outside of the device. In one embodiment, a master controller creates a table of values which follow the desired minimum, maximum, mean, and standard deviation, etc. of the particular desired statistical distribution required. The created table is then communicated to the limited capacity device and can be used whenever a distribution of random values is required. The master controller could have one of several slave devices associated with it in the system. In another embodiment, where the storage capability of the device is large enough to store a table of values with sufficient different entries to create a distribution of satisfactory "randomness" for the particular application, a random number generator within the device is used to select the order of presentation of the table of values.