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September, 1960 Graphs for Bivariate Normal Probabilities
Marvin Zelen, Norman C. Severo
Ann. Math. Statist. 31(3): 619-624 (September, 1960). DOI: 10.1214/aoms/1177705789


Recently there has been much activity dealing with the tabulation of the bivariate normal probability integral. D. B. Owen [3], [4] has summarized many of the properties of the bivariate normal distribution function and tabulated an auxiliary function which enables one to calculate the bivariate normal probability integral. In addition, the National Bureau of Standards [1] has compiled extensive tables of the bivariate normal integral drawn from the works of K. Pearson, Evelyn Fix and J. Neyman, and H. H. Germond. In this same volume, D. B. Owen has contributed an extensive section on applications. It is the purpose of this paper to present three charts, which will enable one to easily compute the bivariate normal integral to a maximum error of $10^{-2}$. This should be sufficient for most practical applications. Owen and Wiesen [5] have also presented charts with a similar objective; however, as pointed out below, we believe the charts presented here lend themselves more easily to visual interpolation. Actually the motivation for these charts came from the Owen and Wiesen work.


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Marvin Zelen. Norman C. Severo. "Graphs for Bivariate Normal Probabilities." Ann. Math. Statist. 31 (3) 619 - 624, September, 1960.


Published: September, 1960
First available in Project Euclid: 27 April 2007

zbMATH: 0090.11503
MathSciNet: MR128614
Digital Object Identifier: 10.1214/aoms/1177705789

Rights: Copyright © 1960 Institute of Mathematical Statistics

Vol.31 • No. 3 • September, 1960
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