algorithms: Choice of Algorithm and Hyper Parameters

algorithmsR Documentation

Choice of Algorithm and Hyper Parameters


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 = 1e-6)



maximum number of function values as integer. The internal FORTRAN code always uses a minimum number depending on the dimension. (for example 752 for three-dimensional problems).


absolute error tolerance; for TVPACK only used for dimension 3.


relative error tolerance as double.


number of grid points to be evaluated; cannot be larger than 4097.


logical indicating if a check for singularity of the correlation matrix should be performed (once per function call to pmvt() or pmvnorm()).


replacement for Inf when non-orthant probabilities involving Inf shall be computed.


There are three algorithms available for evaluating normal (and two algorithms for t-) probabilities: The default is the randomized Quasi-Monte-Carlo 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 non-singular 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). Non-orthant probabilities are computed from the corresponding orthant probabilities, however, infinite limits are replaced by maxval along with a warning.

For two- and three-dimensional problems and semi-infinite 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 t-probabilities. Journal of Computational and Graphical Statistics, 11, 950–971.

Genz, A. (2004), Numerical computation of rectangular bivariate and trivariate normal and t-probabilities, 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. Springer-Verlag, Heidelberg.

Miwa, A., Hayter J. and Kuriki, S. (2003). The evaluation of general non-centred 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.

mvtnorm documentation built on May 29, 2024, 12:29 p.m.