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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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An evaluation of the integral of the product of the error function and the normal probability density with application to the bivariate normal integral
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by Hatem A. Fayed and Amir F. Atiya PDF
Math. Comp. 83 (2014), 235-250 Request permission

Abstract:

This paper derives the value of the integral of the product of the error function and the normal probability density as a series of the Hermite polynomial and the normalized incomplete Gamma function. This expression is beneficial, and can be used for evaluating the bivariate normal integral as a series expansion. This expansion is a good alternative to the well-known tetrachoric series, when the correlation coefficient, $\rho$, is large in absolute value.
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Additional Information
  • Hatem A. Fayed
  • Affiliation: Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Cairo, Egypt 12613
  • Email: h{_}fayed@eng.cu.edu.eg
  • Amir F. Atiya
  • Affiliation: Department of Computer Engineering, Faculty of Engineering, Cairo University, Cairo, Egypt 12613
  • Email: amir@alumni.caltech.edu
  • Received by editor(s): October 5, 2011
  • Received by editor(s) in revised form: February 20, 2012
  • Published electronically: May 29, 2013
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 235-250
  • MSC (2010): Primary 33B20, 33C45
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02720-2
  • MathSciNet review: 3120588