A novel series expansion for the multivariate normal probability integrals based on Fourier series

DOI10.1090/S0025-5718-2014-02844-5zbMath1298.42004OpenAlexW2074823092MaRDI QIDQ3189426

Hatem A. Fayed, Amir F. Atiya

Publication date: 10 September 2014

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2014-02844-5

zbMATH Keywords

Fourier seriestetrachoric seriesmultivariate normal probability integral

Mathematics Subject Classification ID

Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Multivariate analysis and fuzziness (62H86)

Related Items (2)

An \(O(N)\) algorithm for computing expectation of \(N\)-dimensional truncated multi-variate normal distribution. I: Fundamentals ⋮ The evaluation of bivariate normal probabilities for failure of parallel systems

Uses Software

• Algorithm 462
• QSIMVN

Cites Work

• Calculation of univariate and bivariate normal probability functions
• Computation of multivariate normal and \(t\) probabilities
• The use of the tetrachoric series for evaluating multivariate normal probabilities
• Three digit accurate multiple normal probabilities
• The multivariate normal distribution
• An evaluation of the integral of the product of the error function and the normal probability density with application to the bivariate normal integral
• Tables for Computing Bivariate Normal Probabilities
• Computation of the Bivariate Normal Integral
• The Evaluation of General Non-Centred Orthant Probabilities
• Probability Integrals of Multivariate Normal and Multivariate $t^1$
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