# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

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

noahb320@gmail.com

emmyb320@bu.edu

ResourceFunction["RunCountRandomnessTest"][ counts the number of increasing runs to assess randomness of | |

ResourceFunction["RunCountRandomnessTest"][ counts the number of increasing runs to assess randomness and returns the specified property. |

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.

Generate a sequence of random integers:

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Visualize the sequence:

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Apply a run count-based test to the sequence:

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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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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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Visualize the sampling distribution of the test statistic:

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- 1.0.0 – 08 July 2019

This work is licensed under a Creative Commons Attribution 4.0 International License