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December, 1964 Orthant Probabilities for the Quadrivariate Normal Distribution
I. G. Abrahamson
Ann. Math. Statist. 35(4): 1685-1703 (December, 1964). DOI: 10.1214/aoms/1177700391


Let $x_1, x_2, x_3, x_4$ be jointly distributed with a quadrivariate normal distribution with mean 0, and correlation matrix $\{\rho_{ij}\}$. The orthant probability, i.e. the probability that all the $x_i$'s will be simultaneously positive, is not, in general, given by a closed expression; but is easily computed in a special class of cases, here called orthoscheme probabilities. It is explicitly shown how the general orthant probability can be expressed as a linear combination of six orthoscheme probabilities. Orthoscheme probabilities have been tabulated by the author and instructions for the use of this table [1] are given. In addition, an abridged table is appended.


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I. G. Abrahamson. "Orthant Probabilities for the Quadrivariate Normal Distribution." Ann. Math. Statist. 35 (4) 1685 - 1703, December, 1964.


Published: December, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0125.09102
MathSciNet: MR166856
Digital Object Identifier: 10.1214/aoms/1177700391

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 4 • December, 1964
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