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A new approach to analyze the independence of statistical tests of randomness

Author

Listed:
  • Almaraz Luengo, Elena
  • Leiva Cerna, Marcos Brian
  • García Villalba, Luis Javier
  • Hernandez-Castro, Julio

Abstract

One of the fundamental aspects when working with batteries of statistic tests is that they should be as efficient as possible, i.e. that they should check the properties and do so in a reasonable computational time. This assumes that there are no tests that are checking the same properties, i.e. that they are not correlated. One of the most commonly used measures to verify the interrelation between variables is the Pearson’s correlation. In this case, linear dependencies are checked, but it may be interesting to verify other types of non-linear relationships between variables. For this purpose, mutual information has recently been proposed, which measures how much information, on average, one random variable provides to another. In this work we analyze some well-known batteries by using correlation analysis and mutual information approaches.

Suggested Citation

  • Almaraz Luengo, Elena & Leiva Cerna, Marcos Brian & García Villalba, Luis Javier & Hernandez-Castro, Julio, 2022. "A new approach to analyze the independence of statistical tests of randomness," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    • Handle: RePEc:eee:apmaco:v:426:y:2022:i:c:s0096300322002004
    DOI: 10.1016/j.amc.2022.127116
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    References listed on IDEAS

    as
    1. Marsaglia, George & Tsang, Wai Wan, 2002. "Some Difficult-to-pass Tests of Randomness," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 7(i03).
    2. Laeuchli, Jesse & Ramírez-Cruz, Yunior & Trujillo-Rasua, Rolando, 2022. "Analysis of centrality measures under differential privacy models," Applied Mathematics and Computation, Elsevier, vol. 412(C).
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