DIEHARD Suite of Tests and Random Number Generation

Many areas of statistical analysis, research, and simulation rely on the quality of random number generators. Most programs for statistical data analysis contain a function for generating uniform random numbers. A recent review of statistical packages (McCullough, 1998, 1999) that appeared in The American Statistician tested the random number generators of several programs using the so-called DIEHARD suite of tests (Marsaglia, 1998). DIEHARD applies various methods of assembling and combining uniform random numbers, and then performs statistical tests that are expected to be nonsignificant; this suite of tests has become a standard method of evaluating the quality of uniform random number generator routines.

The random number generators in Statistica have been certified using the DIEHARD suite of tests, and they passed all the test criteria.

It should be pointed out that the DIEHARD suite of tests applies various approaches in order to detect nonrandomness in the stream of (supposedly) uniform random numbers, and success (passing all tests) is by no means guaranteed. For example, in the review by McCullough (1999), several other commonly used statistics packages failed at least one of the tests ("Count the Ones Test"), and some failed more than one test (see Table 2, p. 156, of McCullough, 1999).

In summary, because of the quality of its random number generators, the Statistica programming environment is suitable, for example, for Monte Carlo simulations or analyses using advanced Bayesian methods.