A Note on the Generation of Random Normal Deviates

By G. Box, M. E. Muller. 1958

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Citations in the corpus

A Comprehensive Comparison of Multiparty Secure Additions with Differential Privacy (2015, background): “Generating a random variable from the Gaussian distribution requires, on average, drawing a single uniformly distributed number [6].”
Fire dynamics simulator technical reference guide volume 1 :: mathematical model (2013, methodology): “In FDS, ζ (t) are generated from a Box-Muller transform [93].”
The Effects of Type I Error Rate and Power of the ANCOVA F Test and Selected Alternatives Under Nonnormality and Variance Heterogeneity (2001, methodology): “Two streams of data were generated from the SAS RANNOR function, in which one uses the Box and Muller (1958) transformation to create standard normal random variables.”
Dr. Probe: A software for high-resolution STEM image simulation. (2018, methodology): “The random displacements follow a normal probability distribution implemented by Box-Muller transformation of uniformly distributed pseudo-random numbers [33].”
Secure multiparty aggregation with differential privacy: a comparative study (2013, background): “Generating a random variable from the Gaussian distribution requires, on average, drawing from uniform distribution only one random variable [5].”
Ant colony optimization: Introduction and recent trends (2005, methodology): “The sampling of the chosen Gaussian function j∗ may be done using a random number generator that is able to generate random numbers according to a parameterized normal distribution, or by using a uniform random generator in conjunction with (for instance) the Box–Muller method [18].”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, background): “Transforming these back into x and y gives us the Box-Muller method described in Fig.”
Geometric Approximation Algorithms (2011, methodology): “Given a source of random numbers according to the uniform distribution, this can be done using a O(1) computations, using the Box-Muller transformation [BM58].”