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).
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 Quasi-Monte-Carlo 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 non-singular covariance matrices,
the algorithm by Miwa et al. (2003) can be used as well.
For two- and three-dimensional problems and semi-infinite 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, 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.