Random Number Tests

If one is using random numbers during simulation to generate pseudo-number generators it is important to check the 'quality' of these pseudo-random numbers. Donald E.Knuth [179] gives in chapt.3 a list of applicable tests in such a situation.

Generally it is assumed that the base numbers are assumed to be independent and uniformly distributed either as reals between zero and one or as integers between zero and some d-1.

  1. Theoretical: Chi-square test ($ \chi^{2}$) applies to the situation when observations can fall into a finite number of categories
  2. Empirical: Equidistribution test (Knuth [179]:59f. In the wood1-scenario we have a move generator producing a random number $ r$ out of the set $ \{0, ..., 8\}$. In a first step one has to count the number of occurences $ n_{r.i}$ for each possible pseudo random number $ r_{i} \in \{0, ..., 8\}$. Then one has to apply the chi-square test (see above).
  3. Empirical: Serial test
  4. Empirical: Partition test
  5. Empirical: Coupon Collector's test
  6. Empirical: Permutation test
  7. Empirical: Run test
  8. Empirical: Maximum-of-t test
  9. Empirical: Serial Correlation test
  10. Empirical: test on subsequences



Subsections
Gerd Doeben-Henisch 2012-03-31