A simple generalization of the Box–Muller method for obtaining a pair of correlated standard normal variables

Dias, J. Rodrigues

doi:10.1080/00949650902839162

Cited by 6 publications

(1 citation statement)

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“…Among these methods, Box-Muller method is widely used because of its easy implementation procedure and high efficiency, which produces independent and exact samples from Gaussian density. However, generating non-standard multivariate Gaussian density ( ), is the dimension, under the current setting of Box-Muller method is not discovered yet 2 .…”

Section: Introductionmentioning

confidence: 99%

Efficient Generation of Gaussian Varaiates Via Acceptance-Rejection Framework

Sajib

2019

Dhaka Univ. J. Sci.

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The Gaussian distribution is often considered to be the underlying distribution of many observed samples for modelling purposes, and hence simulation from the Gaussian density is required to verify the fitted model. Several methods, most importantly, Box-Muller method, inverse transformation method and acceptance-rejection method devised by Box and Muller1, Rao et al.7 and Sigman8 respectively, are available in the literature to generate samples from the Gaussian distribution. Among these methods, Box-Muller method is the most popular and widely used because of its easy implementation and high efficiency,which produces exact samples2. However, generalizing this method for generating non-standard multivariate Gaussian variates is not discovered yet. On the other hand, inverse transformation method uses numerical approximation to the CDF of Gaussian density which may not be desirable in some situations while performance of acceptance-rejection method depends on choosing efficient proposal density. In this paper, we introduce a more general technique by exploiting the idea invented by Wakefield9 under acceptance rejection framework to generate one dimensional Gaussian variates, in which we don’t require to choose any proposal density and it can be extended easily for non-standard multivariate Gaussian density. The proposed method is compared to the existing acceptance-rejection method (Sigman8 method), and we have shown both mathematically and empirically that the proposed method performs better than Sigman8 method as it has a higher acceptance rate (79.53 %) compared to Sigman (76.04 %) method. Dhaka Univ. J. Sci. 67(2): 123-130, 2019 (July)

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Section: Introductionmentioning

confidence: 99%