Abstract
Generators of uniformly distributed random numbers are broadly applied in simulations of stochastic processes that rely on normal and other distributions. In a point of fact, the uniform random numbers are actively used for applications that range from, modeling different phenomena such as theoretical mathematics and technical designing, to evidence-based medicine. This paper proposes a novel approach which consists of a combination of global twister with circular technique and initial congruential generation with complete stochastic sequences. It has been experimentally confirmed that for complete sequences this type of generation provides uniformity in distribution of random numbers. The offered program codes include the tuning methods for the generation technique where random numbers may take any bit length. Moreover, the automatic switching of generator parameters such as initial congruential constants depending on intervals for generated numbers is considered as well. Demonstrated results of testing confirm the uniformity of distribution without any repeated or skipped generated elements.
Highlights
In the beginning we started with the fact that congruential technique of random number generation can’t provide the uniform distribution for all congruential constants and initial values in the linear function xi+1 =mod m
The result may be improved to uniform distribution if complete sequences are considered in the assumption that total amount of random numbers is N = m
To speed up the calculation capability for complete sequences the modulus operation may be changed to the operation of bit conjunction (&) with a mask having w = log2N of bit length
Summary
A Pseudorandom Number Generators (PRNG) are well-known techniques with broad applications in such areas as cryptography (Tusnoo et al, 2003; Ozturk et al, 2004; Panneton et al, 2006), simulation of stochastic processes (Entacher, 1998), comprehensive testing of technical systems (Leeb and Wegenkittl, 1997; Park and Miller, 1998), medical (Menyaev and Zharov, 2006a; 2006b; Menyaev and Zharova, 2006; Menyaev et al, 2006; 2013; 2016; Sarimollaoglu et al, 2014; Cai et al, 2016a; 2016b) and biological research (Wiese et al, 2005; Leonard and Jackson, 2015; Juratly et al, 2015; 2016) and others (Rababbah 2004; 2007; Politano et al, 2014; 2016; Riguzzi, 2016). The issue of the repeatability of elements within a given time period and question of completeness of sets with elements are important and remain to be discussed
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