Twister Generator of Random Normal Numbers by Box-Muller Model

Abstract

Twisting generators of the pseudorandom normal variables can use uniform random sequences as a basis. However, such technique could provide poor quality result in cases where the original sequences have insufficient uniformity or skipping of random values. This work offers a new approach for creating the random normal variables using the Box-Muller model as a basis together with the twisting generator of uniform planes. The simulation results confirm that the random variables obtained have a better approximation to normal Gaussian distribution. Moreover, combining this new approach with the tuning algorithm of basic twisting generation allows for a significantly increased the length of created sequences without using any additional random access memory of the computer.

Phase Congruential White Noise Generator

“…Using Expressions (35) and (36), the random phases ψ k or ϕ k are determined by the congruential technology [45][46][47][48][49][50] using corresponding integer random variable x cong k :…”

“…Below is the program P070502, which also uses the same number of N S countings. They were created earlier in the program P070401 (in subsection Construction and Results) by using congruential technology [45][46][47][48][49][50] in the generator cDeonYuliCongPhase62A. The listing of the results demonstrates that the signal contains N s = 33 countings and N F = 16 Fourier frequencies.…”

“…In our previous articles [45][46][47][48][49][50], we thoroughly explored the capabilities of new congruential and twister generators, which ensure absolute completeness and uniformity of integer random variable distribution. Based on the main principles outlined in [45][46][47][48][49][50], further here we have established a new generator, which is specially designed to implement the white noise process with the above mentioned properties. In accordance with this, below is the basic generator cDeonYuliCongBase62 and on its basis the derived congruential generator cDeonYuliCongSequence62.…”

Designing the Uniform Stochastic Photomatrix Therapeutic Systems

“…Moving further, it could be be noted that Expression (28) also has some limitations. The first of which concerns the number N. Our mathematical studies [46][47][48][49][50][51] show that uniform generation is achieved only at the condition of N = 2 w . The exponent w exactly matches the quantity of the required binary bits, which are needed for representing the decimal number N − 1.…”

“…Particularly for the current issue, i.e., in case of PMTS influence on biological tissue, this means an accurate understanding of the uniform operation of randomly turned on LEDs. The term 'uniform random variables' means that in the allotted time, all the exposure elements (LEDs or their analogues) are switched on precisely the same number of times [46][47][48][49][50][51]. Thus, it should be started with this, i.e., by checking the ability of standard tools to ensure the uniform generation of irradiation from point light sources.…”