Topic
Box–Muller transform
About: Box–Muller transform is a research topic. Over the lifetime, 36 publications have been published within this topic receiving 492 citations. The topic is also known as: Box–Muller's method.
Papers
TL;DR: A simple, easy to implement numerical method for generating random deviates from a q-Gaussian distribution based upon a generalization of the well known Box-Miiller method is developed and presented.
Abstract: The q-Gaussian distribution is known to be an attractor of certain correlated systems and is the distribution which, under appropriate constraints, maximizes a generalization of the familiar Shannon entropy. This generalized entropy, or q-entropy, provides the basis of nonextensive statistical mechanics, a theory which is postulated as a natural extension of the standard (Boltzmann-Gibbs) statistical mechanics, and which may explain the ubiquitous appearance of heavy-tailed distributions in both natural and man-made systems. The q-Gaussian distribution is also used as a numerical tool, for example as a visiting distribution in Generalized Simulated Annealing. A simple, easy to implement numerical method for generating random deviates from a q-Gaussian distribution based upon a generalization of the well known Box-Miiller method is developed and presented. This method is suitable for a larger range of q values, -infin < q < 3, than has previously appeared in the literature, and can generate deviates from q-Gaussian distributions of arbitrary width and center. MATLAB code showing a straightforward implementation is also included.
106 citations
TL;DR: In this article, a sample of size 1,000,000 was used for Monte Carlo analysis, and it was shown that the observed frequencies are not following the expected pattern and that the sampling distribution has marked local maxima approximately at the points -33, 3 0 and 3-6.
Abstract: SUMMARY In a recent Monte Carlo study, a most unsatisfactory sampling distribution was obtained when supposedly standard techniques were employed to simulate a simple random sample from the standard normal distribution A selection of observed and expected frequencies (the latter rounded to the nearest integer) in the tails of the distribution for a sample of size 1,000,000 is given in Table 1 It hardly needs a chi-square test to indicate that the observed frequencies are not following the expected pattern! Note particularly that all the 1,000,000 observations are restricted to the range (-333 36), and that the sampling distribution has marked local maxima approximately at the points - 33, 3 0 and 3-6 This paper investigates such phenomena
73 citations
Journal Article•
63 citations
TL;DR: It is proved that the Box-Muller method can be used with low-discrepancy sequences, and when its use could actually be advantageous is discussed.
53 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 1 |
| 2015 | 1 |
| 2014 | 2 |