ABSTRACT
This chapter describes certain standard tests for uniform random digits and shows the results of applying these tests to sequences resulting from a variety of generators. A property of a pseudo-random number generator for its entire cycle provides, effectively, a test of that generator, and a test of a kind that is not possible for physical random number generators. The mean and variance of Poisson random variables are equal, and the index of dispersion test makes use of this result to provide a particular test for the Poisson distribution. A striking feature of a table of digits can be the occurrence of runs of the same digit. If such runs occur with greater frequency than one would expect for random digits then one might expect this feature to result in a significant departure from the geometric distribution of the gap test.
