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Correlations in random numbers generators: Good's serial test

For each of 200 samples, each sample has 10000 variates, we take an overlapping pairs of numbers. The N-1 points ( \( \xi _{i},\xi _{i+1} \)), i=1,...,N-1 were histogrammed into k\( ^{2} \) sub squares with k=16, so for each from 16\( ^{2} \)subsquares we have number n\( _{i,j} \),i=1..16,j=1..16, which equals number of occurencies of pairs in those square. the following quantities were formed,

e\( _{1}=(N-1)/k, \) e\( _{2}=e1/k, \) c \( _{i}=\sum ^{k}_{j=1}n_{ij} \)

t\( _{1}\protect \)= \( \sum ^{k}(c_{ii=1}-e_{1})^{2}/e_{1} \)

and

t \( _{2}=\sum _{i=1}^{k}\sum _{j=1}^{k}(n_{ij}-e_{2})^{2}/e_{1} \)

The statistic w is defined by

w=t\( _{2}- \)t\( _{1}\protect \)



Subsections

Amaury LATAILLADE 2002-11-04