Version 1
: Received: 24 September 2021 / Approved: 28 September 2021 / Online: 28 September 2021 (09:56:55 CEST)
How to cite:
Oliveira, H. Deterministic Sampling from Univariate Normal Distributions with Sierpinski Space-Filling Curves. Preprints2021, 2021090460. https://doi.org/10.20944/preprints202109.0460.v1
Oliveira, H. Deterministic Sampling from Univariate Normal Distributions with Sierpinski Space-Filling Curves. Preprints 2021, 2021090460. https://doi.org/10.20944/preprints202109.0460.v1
Oliveira, H. Deterministic Sampling from Univariate Normal Distributions with Sierpinski Space-Filling Curves. Preprints2021, 2021090460. https://doi.org/10.20944/preprints202109.0460.v1
APA Style
Oliveira, H. (2021). Deterministic Sampling from Univariate Normal Distributions with Sierpinski Space-Filling Curves. Preprints. https://doi.org/10.20944/preprints202109.0460.v1
Chicago/Turabian Style
Oliveira, H. 2021 "Deterministic Sampling from Univariate Normal Distributions with Sierpinski Space-Filling Curves" Preprints. https://doi.org/10.20944/preprints202109.0460.v1
Abstract
This work addresses the problem of sampling from Gaussian probability distributions by means of uniform samples obtained deterministically and directly from space-filling curves (SFCs), a purely topological concept. To that end, the well-known inverse cumulative distribution function method is used, with the help of the probit function,which is the inverse of the cumulative distribution function of the standard normal distribution. Mainly due to the central limit theorem, the Gaussian distribution plays a fundamental role in probability theory and related areas, and that is why it has been chosen to be studied in the present paper. Numerical distributions (histograms) obtained with the proposed method, and in several levels of granularity, are compared to the theoretical normal PDF, along with other already established sampling methods, all using the cited probit function. Final results are validated with the Kullback-Leibler and two other divergence measures, and it will be possible to draw conclusions about the adequacy of the presented paradigm. As is amply known, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. That said, sequences resulting from this kind of procedure are not truly random. Even so, and to be coherent with the literature, the expression ”random number” will be used along the text to mean ”pseudo-random number”.
Keywords
Space-filling curves; Ergodic Theory; random number generation; Gaussian distribution
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
