Natural Test for Random Numbers Generator Based on Exponential Distribution

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<sup>...

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Main Authors:	Ilija Tanackov, Feta Sinani, Miomir Stanković, Vuk Bogdanović, Željko Stević, Mladen Vidić, Jelena Mihaljev-Martinov
Format:	Article
Language:	English
Published:	MDPI AG 2019-10-01
Series:	Mathematics
Subjects:	uniform distribution memoryless entropy pseudo-random number generator
Online Access:	https://www.mdpi.com/2227-7390/7/10/920

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spelling	doaj-e704e19bcaea46aea53a1429a989a6512020-11-25T00:09:54ZengMDPI AGMathematics2227-73902019-10-0171092010.3390/math7100920math7100920Natural Test for Random Numbers Generator Based on Exponential DistributionIlija Tanackov0Feta Sinani1Miomir Stanković2Vuk Bogdanović3Željko Stević4Mladen Vidić5Jelena Mihaljev-Martinov6Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, SerbiaFaculty of Applied Sciences, State University of Tetova, Ilindenska 1000, 1200 Tetovo, North MacedoniaMathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001 Belgrade, SerbiaFaculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, SerbiaFaculty of Transport and Traffic Engineering Doboj, University of East Sarajevo, Vojvode Mišića 52, 74000 Doboj, Bosnia and HerzegovinaFaculty of Transport and Traffic Engineering Doboj, University of East Sarajevo, Vojvode Mišića 52, 74000 Doboj, Bosnia and HerzegovinaFaculty of Medicine, University of Novi Sad, Hajduk Veljkova 3, 21000 Novi Sad, SerbiaWe 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<sup>−1</sup>. 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 <i>e</i> = 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.https://www.mdpi.com/2227-7390/7/10/920uniform distributionmemorylessentropypseudo-random number generator
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Ilija Tanackov Feta Sinani Miomir Stanković Vuk Bogdanović Željko Stević Mladen Vidić Jelena Mihaljev-Martinov
spellingShingle	Ilija Tanackov Feta Sinani Miomir Stanković Vuk Bogdanović Željko Stević Mladen Vidić Jelena Mihaljev-Martinov Natural Test for Random Numbers Generator Based on Exponential Distribution Mathematics uniform distribution memoryless entropy pseudo-random number generator
author_facet	Ilija Tanackov Feta Sinani Miomir Stanković Vuk Bogdanović Željko Stević Mladen Vidić Jelena Mihaljev-Martinov
author_sort	Ilija Tanackov
title	Natural Test for Random Numbers Generator Based on Exponential Distribution
title_short	Natural Test for Random Numbers Generator Based on Exponential Distribution
title_full	Natural Test for Random Numbers Generator Based on Exponential Distribution
title_fullStr	Natural Test for Random Numbers Generator Based on Exponential Distribution
title_full_unstemmed	Natural Test for Random Numbers Generator Based on Exponential Distribution
title_sort	natural test for random numbers generator based on exponential distribution
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-10-01
description	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<sup>−1</sup>. 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 <i>e</i> = 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.
topic	uniform distribution memoryless entropy pseudo-random number generator
url	https://www.mdpi.com/2227-7390/7/10/920
work_keys_str_mv	AT ilijatanackov naturaltestforrandomnumbersgeneratorbasedonexponentialdistribution AT fetasinani naturaltestforrandomnumbersgeneratorbasedonexponentialdistribution AT miomirstankovic naturaltestforrandomnumbersgeneratorbasedonexponentialdistribution AT vukbogdanovic naturaltestforrandomnumbersgeneratorbasedonexponentialdistribution AT zeljkostevic naturaltestforrandomnumbersgeneratorbasedonexponentialdistribution AT mladenvidic naturaltestforrandomnumbersgeneratorbasedonexponentialdistribution AT jelenamihaljevmartinov naturaltestforrandomnumbersgeneratorbasedonexponentialdistribution
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Natural Test for Random Numbers Generator Based on Exponential Distribution

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