Function Repository Resource:

RunCountRandomnessTest

Source Notebook

Conduct a runs up–based randomness test on a sequence of random reals between 0 and 1

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

ResourceFunction["RunCountRandomnessTest"][sequence]

counts the number of increasing runs to assess randomness of sequence and returns an associated p-value.

ResourceFunction["RunCountRandomnessTest"][sequence,"property"]

counts the number of increasing runs to assess randomness and returns the specified 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 creating a chi square–like statistic that measures the difference between the counts of runs up in a sequence and the expected mean counts of runs up in the sequence.

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

ResourceFunction["RunCountRandomnessTest"] results are valid only for sequence lengths greater than 600.

The ResourceFunction["RunCountRandomnessTest"] function performs a two-tailed test on the test statistic.

Examples

Basic Examples (3)

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 run count-based test to the sequence:

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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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Possible Issues (1)

This test is not very powerful and fails to reject non-random sequences that repeat over longer intervals on occasion. Ideally, it should be used in conjunction with another test:

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