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Natural Test for Random Numbers Generator Based on Exponential Distribution

Author

Listed:
  • Ilija Tanackov

    (Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia)

  • Feta Sinani

    (Faculty of Applied Sciences, State University of Tetova, Ilindenska 1000, 1200 Tetovo, North Macedonia)

  • Miomir Stanković

    (Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001 Belgrade, Serbia)

  • Vuk Bogdanović

    (Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia)

  • Željko Stević

    (Faculty of Transport and Traffic Engineering Doboj, University of East Sarajevo, Vojvode Mišića 52, 74000 Doboj, Bosnia and Herzegovina)

  • Mladen Vidić

    (Faculty of Transport and Traffic Engineering Doboj, University of East Sarajevo, Vojvode Mišića 52, 74000 Doboj, Bosnia and Herzegovina)

  • Jelena Mihaljev-Martinov

    (Faculty of Medicine, University of Novi Sad, Hajduk Veljkova 3, 21000 Novi Sad, Serbia)

Abstract

We will prove that when uniformly distributed random numbers are sorted by value, their successive differences are a exponentially distributed random variable Ex(λ). For a set of n random numbers, the parameters of mathematical expectation and standard deviation is λ = n −1 . The theorem was verified on four series of 200 sets of 101 random numbers each. The first series was obtained on the basis of decimals of the constant e = 2.718281…, the second on the decimals of the constant π = 3.141592…, the third on a Pseudo Random Number generated from Excel function RAND, and the fourth series of True Random Number generated from atmospheric noise. The obtained results confirm the application of the derived theorem in practice.

Suggested Citation

  • Ilija Tanackov & Feta Sinani & Miomir Stanković & Vuk Bogdanović & Željko Stević & Mladen Vidić & Jelena Mihaljev-Martinov, 2019. "Natural Test for Random Numbers Generator Based on Exponential Distribution," Mathematics, MDPI, vol. 7(10), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:920-:d:273117
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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. B. D. McCullough, 2006. "A review of TESTU01," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 677-682, July.
    3. Van Bever, Germain, 2016. "Simplicial bivariate tests for randomness," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 20-25.
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