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.References
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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