Function Repository Resource:

SpectralRandomnessTest

Use a discrete cosine transform–based method to test the randomness of a sequence of random reals

Contributed by: Emmy/Noah Blumenthal
noahb320@gmail.com
emmyb320@bu.edu

ResourceFunction["SpectralRandomnessTest"][sequence]

conducts a discrete cosine transform-based test to asses the randomness of either a sequence of 0s and 1s or reals between 0 and 1, returning the associated p-value.

ResourceFunction["SpectralRandomnessTest"][sequence,"property"]

conducts a discrete cosine transform-based test and returns the associated property.

Details and Options

Properties include:

"TestStatistic"

returns the test statistic

"PValue"

returns the p-value associated with the test

The test statistic is generated by comparing the discrete cosine transformed data with the normal distribution using the Kolmogorov-Smirnov test.

The test works for sequences of of random reals between 0 and 1 and sequences of only 0s and 1s

Examples

Basic Examples (2)

Generate a sequence of random integers:

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Visualize the sequence:

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$ArrayPlot[Partition[sequence, 16]\[Transpose], Sequence[ ImageSize -> Large, ColorFunction -> "CandyColors"]]$

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Apply a discrete cosine transform-based test:

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Generate a sequence of random integers:

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Visualize the sequence:

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$ArrayPlot[Partition[sequence, 16]\[Transpose], Sequence[ ImageSize -> Large, ColorFunction -> "CandyColors"]]$

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Apply a discrete cosine transform-based test:

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Scope (3)

Generate a sequence of random integers:

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Visualize the sequence:

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Attempt to reject a non-random sequence:

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Applications (1)

Test to see if rule 30 is random according to the spectral test:

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$rule30seq = CellularAutomaton[30, {{1}, 0}, {10000, 0}]\[Transpose][[1]];$

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Possible Issues (1)

For non-random data, the Kolmogorov–Smirnov test, a part of the entire test, may return ties. Observing such ties is a strong indicator that the data is non-random:

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