@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 numerical_methods},
  mrclass = {60.0X},
  mrnumber = {0065047 (16,377c)},
  mrreviewer = {L. Weiss},
  pages = {351--360},
  timestamp = {2012-10-18T06:54:51.000+0200},
  title = {A reduction formula for normal multivariate integrals},
  volume = 41,
  year = 1954
}