Evaluation of the normal distribution function

Martynov, G. V.

doi:10.1007/bf01085187

Cited by 14 publications

(4 citation statements)

References 87 publications

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“…Gupta (1963) provided a complete bibliography on the topic. Martynov (1981) presented a survey of recent developments in the evaluation of multivariate normal integrals. He concluded that "in the general case a satisfactory solution of it has so far not been found".…”

Section: Wangmentioning

confidence: 99%

An approximation of multivariate normal orthant probabilities of dimension 4: a contingency-table approach

Vang

1987

Comm. in Stats. - Simulation & Comp.

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Section: Wangmentioning

confidence: 99%

An approximation of multivariate normal orthant probabilities of dimension 4: a contingency-table approach

Vang

1987

Comm. in Stats. - Simulation & Comp.

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“…A survey of the literature on computing the standard normal distribution was given by Martynov [1981], and a more modern review is given by Marsaglia [2004]. This latter gives a table-free C function to compute the normal distribution with error less than 8 × 10 −16 , and along with Zeileis and Kleiber [2005], Marsaglia points out there remain problems with various implementations for the error function and standard normal distribution.…”

Section: Introductionmentioning

confidence: 98%

Algorithm 885

Linhart

2008

ACM Trans. Math. Softw.

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We present and compare three C functions to compute the logarithm of the cumulative standard normal distribution. The first is a new algorithm derived from Algorithm 304's calculation of the standard normal distribution via a series or continued fraction approximation, and it is good to the accuracy of the machine. The second is based on Algorithm 715's calculation of the standard normal distribution via rational Chebyshev approximation. This is related to, and an improvement on, the algorithm for the logarithm of the normal distribution available in the software package R. The third is a new and simple algorithm that uses the compiler's implementation of the error function, and complement of the error function, to compute the log of the normal distribution.

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“…This is a natural setting of wide interest in probability, statistics and theoretical computer science. Integrating multivariate Gaussian distributions has been studied for many decades and has a wide variety of applications for statistics [13,31,15,34,14]. It appears to be at least as important as the special case of computing the volume of convex body.…”

Section: Introductionmentioning

confidence: 99%

A Cubic Algorithm for Computing Gaussian Volume

Cousins¹,

Vempala²

2013

Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms

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We present randomized algorithms for sampling the standard Gaussian distribution restricted to a convex set and for estimating the Gaussian measure of a convex set, in the general membership oracle model. The complexity of the integration algorithm is O * (n 3 ) while the complexity of the sampling algorithm is O * (n 3 ) for the first sample and O * (n 2 ) for every subsequent sample. These bounds improve on the corresponding state-of-the-art by a factor of n. Our improvement comes from several aspects: better isoperimetry, smoother annealing, avoiding transformation to isotropic position and the use of the "speedy walk" in the analysis. * Georgia Tech.

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Evaluation of the normal distribution function

Cited by 14 publications

References 87 publications

An approximation of multivariate normal orthant probabilities of dimension 4: a contingency-table approach

An approximation of multivariate normal orthant probabilities of dimension 4: a contingency-table approach

Algorithm 885

A Cubic Algorithm for Computing Gaussian Volume

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