Evaluate

Basic Examples

Generate a sequence of random integers and apply a cumulative sums test:
sequence=RandomInteger[{0,1},1000];
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Visualize the sequence:
ArrayPlotPartition[sequence,16],

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[◼]
CUSUMMaxRandomnessTest
[sequence,"TestStatistic"]
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40
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CUSUMMaxRandomnessTest
[sequence,"PValue"]
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0.411511
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Applications

Reject a non-random sequence:
subsequence=RandomInteger[{0,1},40];
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sequence=Flatten@Table[subsequence,20];
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ArrayPlotPartition[sequence,16],

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[◼]
CUSUMMaxRandomnessTest
[sequence,"TestStatistic"]
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121
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CUSUMMaxRandomnessTest
[sequence,"PValue"]
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0.0000754334
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Test the randomness of rule 30:
rule30seq=CellularAutomaton[30,{{1},0},{100000,0}]〚1〛;
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ArrayPlotPartition[Take[rule30seq,1000],16],

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[◼]
CUSUMMaxRandomnessTest
[rule30seq]
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0.740419
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Possible Issues

CUSUMMaxRandomnessTest requires sequences of length 100 or more:
[◼]
CUSUMMaxRandomnessTest
[RandomInteger[{0,1},50]]
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CUSUMMaxRandomnessTest
::seqlength
:The sequence length is less than 100 bits!

Neat Examples

Visualize the sampling distribution of the test statistic:
samp=Table
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CUSUMMaxRandomnessTest
[RandomInteger[{0,1},1000],"TestStatistic"],1000;
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Histogram[samp,Automatic,"PDF"]
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