algorithms  R Documentation 
Choose between three algorithms for evaluating normal (and t) distributions and define hyper parameters.
GenzBretz(maxpts = 25000, abseps = 0.001, releps = 0)
Miwa(steps = 128, checkCorr = TRUE, maxval = 1e3)
TVPACK(abseps = 1e6)
maxpts 
maximum number of function values as integer. The internal FORTRAN code always uses a minimum number depending on the dimension. (for example 752 for threedimensional problems). 
abseps 
absolute error tolerance; for 
releps 
relative error tolerance as double. 
steps 
number of grid points to be evaluated; cannot be larger than 4097. 
checkCorr 
logical indicating if a check for singularity of the
correlation matrix should be performed (once per function call to

maxval 
replacement for 
There are three algorithms available for evaluating normal (and two algorithms for t) probabilities: The default is the randomized QuasiMonteCarlo procedure by Genz (1992, 1993) and Genz and Bretz (2002) applicable to arbitrary covariance structures and dimensions up to 1000.
For normal probabilities, smaller dimensions (up to 20) and nonsingular
covariance matrices,
the algorithm by Miwa et al. (2003) can be used as well. This algorithm can
compute orthant probabilities (lower
being Inf
or
upper
equal to Inf
). Nonorthant probabilities are computed
from the corresponding orthant probabilities, however, infinite limits are
replaced by maxval
along with a warning.
For two and threedimensional problems and semiinfinite integration
region, TVPACK
implements an interface to the methods described
by Genz (2004).
An object of class "GenzBretz"
, "Miwa"
, or "TVPACK"
defining hyper parameters.
Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1, 141–150.
Genz, A. (1993). Comparison of methods for the computation of multivariate normal probabilities. Computing Science and Statistics, 25, 400–405.
Genz, A. and Bretz, F. (2002), Methods for the computation of multivariate tprobabilities. Journal of Computational and Graphical Statistics, 11, 950–971.
Genz, A. (2004), Numerical computation of rectangular bivariate and trivariate normal and tprobabilities, Statistics and Computing, 14, 251–260.
Genz, A. and Bretz, F. (2009), Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195. SpringerVerlag, Heidelberg.
Miwa, A., Hayter J. and Kuriki, S. (2003). The evaluation of general noncentred orthant probabilities. Journal of the Royal Statistical Society, Ser. B, 65, 223–234.
Mi, X., Miwa, T. and Hothorn, T. (2009).
mvtnorm
: New numerical algorithm for multivariate normal probabilities.
The R Journal 1(1): 37–39.
https://journal.rproject.org/archive/20091/RJournal_20091_Mi+et+al.pdf
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