Testing random Number Sequences

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Testing random Number Sequences

In this section we will test three random number generators with uniform outputs [0,1]. We will compare generator from cecile Unra with standart fortran Ran function, and the Super Duper described above.

In statistics, a GOODNESS OF FIT test used to compare two distributions. For nominal or "binned" measurements, a chi-square test is common. For ordinal or ordered measurements, a Kolmogorov-Smirnov test is appropriate.

We will use these tests for consistency of distribution

Subsections

Testing of uniformity.
- where $\overline{n}=N/k\protect$ , it should follow the $\chi ^{2}\protect$ distribution with $\nu \protect$ =150 degrees of freedom.
Correlations in random numbers generators: Good's serial test
- The distribution of this walues are shown in following pictures with comparision with p $_{\chi ^{2},\nu }(w)\protect$ for $\nu \protect$ =k(k-2)+1= 225 degrees of freedom.
Correlations in random number generators: Correlation coeficients
A composite test for correlations
- should be distributed as
- Taking j=1,10000 non-overlapping pairs from generators were formed, and histogram of 100 bins was formed. Their distribution is compared with its theoretical distribution in following figures
A block test for correlations
- This quantity should follow the chi-square distribution with one degree of freedom. In following figures see the value obtained for the N=10000samples of sequences of different length in the range m=20 to 200 (for unra and ran) resp. m=20 to 400 (super duperand ranecu used in [*]MacKeown). the horizontal line at 3.841 represents the 5% level for the chi-square test with one degree of freedom. No systematic divergence from expectations is seen in either case, and we can be fairly confident of the quality of the variates produced by these generators.
Conclusions

Amaury LATAILLADE 2002-11-04