mvtnorm (version 0.9-8)

algorithms: Choice of Algorithm and Hyper Parameters

Description

Choose between two algorithms for evaluating normal distributions and define hyper parameters.

Usage

GenzBretz(maxpts = 25000, abseps = 0.001, releps = 0)
Miwa(steps = 128)

Arguments

maxpts

maximum number of function values as integer.

abseps

absolute error tolerance as double.

releps

relative error tolerance as double.

steps

number of grid points to be evaluated.

Value

• An object of class GenzBretz or Miwa defining hyper parameters.

Details

There are two 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.

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. 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.