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Date: 20-2-2021
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A multivariate normal distribution in three variables. It has probability density function
(1) |
where
(2) |
The standardized trivariate normal distribution takes unit variances and . The quadrant probability in this special case is then given analytically by
(3) |
(Rose and Smith 1996; Stuart and Ord 1998; Rose and Smith 2002, p. 231).
REFERENCES:
Rose, C. and Smith, M. D. "The Multivariate Normal Distribution." Mathematica J. 6, 32-37, 1996.
Rose, C. and Smith, M. D. "The Trivariate Normal." §6.B A in Mathematical Statistics with Mathematica. New York: Springer-Verlag, pp. 226-228, 2002.
Stuart, A.; and Ord, J. K. Kendall's Advanced Theory of Statistics, Vol. 1: Distribution Theory, 6th ed. New York: Oxford University Press, 1998.
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