Sampling Exactly from the Normal Distribution

DOI10.1145/2710016zbMath1357.65008arXiv1303.6257OpenAlexW1847048756WikidataQ56057952 ScholiaQ56057952MaRDI QIDQ2828164

Charles F. F. Karney

Publication date: 24 October 2016

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.6257

zbMATH Keywords

normal distributionexact samplingrandom deviates

Mathematics Subject Classification ID

Sampling theory, sample surveys (62D05) Monte Carlo methods (65C05) Random number generation in numerical analysis (65C10)

Related Items (13)

The expected bit complexity of the von Neumann rejection algorithm ⋮ Isochronous Gaussian Sampling: From Inception to Implementation ⋮ COSAC: COmpact and Scalable Arbitrary-Centered Discrete Gaussian Sampling over Integers ⋮ Homomorphic Encryption Standard ⋮ An improved exact sampling algorithm for the standard normal distribution ⋮ Secure random sampling in differential privacy ⋮ Faster Gaussian sampling for trapdoor lattices with arbitrary modulus ⋮ Sampling from Arbitrary Centered Discrete Gaussians for Lattice-Based Cryptography ⋮ How to sample a discrete Gaussian (and more) from a random oracle ⋮ Exact sublinear binomial sampling ⋮ Sampling from discrete Gaussians for lattice-based cryptography on a constrained device ⋮ On the rejection rate of exact sampling algorithm for discrete Gaussian distributions over the integers ⋮ Implementation of lattice trapdoors on modules and applications

Uses Software

• MPFR
• MersenneTwister
• Ziggurat
• rnorrexp

Cites Work

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• Sampling from discrete Gaussians for lattice-based cryptography on a constrained device
• Characterizations of a discrete normal distribution
• A Note on the Generation of Random Normal Deviates
• MPFR
• Accuracy in Random Number Generation
• The complexity of generating an exponentially distributed variate
• Algorithm 488: A Gaussian pseudo-random number generator
• Computer Generation of Random Variables Using the Ratio of Uniform Deviates
• Extensions of von Neumann's Method for Generating Random Variables
• Mersenne twister
• A simple method for generating gamma variables
• Von Neumann's Comparison Method for Random Sampling from the Normal and Other Distributions
• Extensions of Forsythe's Method for Random Sampling from the Normal Distribution
• On Buffon Machines and Numbers
• On lattices, learning with errors, random linear codes, and cryptography

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