algorithms
Choice of Algorithm and Hyper Parameters
Choose between three algorithms for evaluating normal distributions and define hyper parameters.
 Keywords
 distribution
Usage
GenzBretz(maxpts = 25000, abseps = 0.001, releps = 0)
Miwa(steps = 128)
TVPACK(abseps = 1e6)
Arguments
 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
TVPACK
only used for dimension 3.  releps
 relative error tolerance as double.
 steps
 number of grid points to be evaluated.
Details
There are three algorithms available for evaluating normal 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 smaller dimensions (up to 20) and nonsingular covariance matrices, the algorithm by Miwa et al. (2003) can be used as well.
For two and threedimensional problems and semiinfinite integration
region, TVPACK
implements an interface to the methods described
by Genz (2004).
Value

An object of class
GenzBretz
or Miwa
defining hyper parameters.
References
Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1, 141150.
Genz, A. (1993). Comparison of methods for the computation of multivariate normal probabilities. Computing Science and Statistics, 25, 400405.
Genz, A. and Bretz, F. (2002), Methods for the computation of multivariate tprobabilities. Journal of Computational and Graphical Statistics, 11, 950971.
Genz, A. (2004), Numerical computation of rectangular bivariate and trivariate normal and tprobabilities, Statistics and Computing, 14, 251260.
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, 223234.
Mi, X., Miwa, T. and Hothorn, T. (2009).
mvtnorm
: New numerical algorithm for multivariate normal probabilities.
The R Journal 1(1): 3739.
http://journal.rproject.org/archive/20091/RJournal_20091_Mi+et+al.pdf