@article{plackett1954reduction,
abstract = {[MR] Let (X1,X2,⋯,Xn) be a vector of chance variables with a nonsingular multivariate normal distribution. The problem is to evaluate P(X1>a1,⋯,Xn>an). The author obtains a reduction formula for this probability, involving integrals of partial derivatives of the probability with respect to the elements of the covariance matrix of (X1,⋯,Xn). For n=3 and n=4, the reduction formula enables the author to express the probability as a finite sum of single integrals of tabulated functions. These integrals have to be evaluated by numerical quadrature, but for certain cases simple approximations to them are given. },
added-at = {2012-10-18T06:54:51.000+0200},
author = {Plackett, R. L.},
biburl = {http://www.bibsonomy.org/bibtex/216aeb1bde598e2e51a73f8acd03edbb0/peter.ralph},
description = {The case of n=2 of the basic identity appears in Pearson 1901, http://archive.org/details/philtrans01501516},
fjournal = {Biometrika},
interhash = {8ed6e6d313cd674ab4b63d818328fe93},
intrahash = {16aeb1bde598e2e51a73f8acd03edbb0},
issn = {0006-3444},
journal = {Biometrika},
keywords = {Gaussian_processes integrals multivariate_Gaussian numerical_methods useful_identity},
mrclass = {60.0X},
mrnumber = {0065047 (16,377c)},
mrreviewer = {L. Weiss},
pages = {351--360},
timestamp = {2015-02-20T02:54:32.000+0100},
title = {A reduction formula for normal multivariate integrals},
url = {http://www.jstor.org/stable/2332716},
volume = 41,
year = 1954
}