Authors: Tanackov, Ilija
Sinani, Feta
Stanković, Miomir 
Bogdanović, Vuk
Stević, Željko
Vidić, Mladen
Mihaljev-Martinov, Jelena
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Natural test for random numbers generator based on exponential distribution
Journal: Mathematics
Volume: 7
Issue: 10
First page: 920
Issue Date: 1-Oct-2019
Rank: ~M21a
ISSN: 2227-7390
DOI: 10.3390/math7100920
© 2019 by the authors. We will prove that when uniformly distributed random numbers are sorted by value, their successive differences are a exponentially distributed random variable Ex(γ). For a set of n random numbers, the parameters of mathematical expectation and standard deviation is γ = 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.
Keywords: Entropy | Memoryless | Pseudo-random number generator | Uniform distribution
Publisher: MDPI
Project: Research of technical-technological, staff and organizational capacity of Serbian Railways, from the viewpoint of current and future European Union requirements 

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