# Choice of Algorithm and Hyper Parameters

### Description

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

### Usage

1 2 3 | ```
GenzBretz(maxpts = 25000, abseps = 0.001, releps = 0)
Miwa(steps = 128)
TVPACK(abseps = 1e-6)
``` |

### 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 three-dimensional problems). |

`abseps` |
absolute error tolerance; for |

`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.

Mi, X., Miwa, T. and Hothorn, T. (2009).
`mvtnorm`

: New numerical algorithm for multivariate normal probabilities.
*The R Journal* **1**(1): 37–39.
http://journal.r-project.org/archive/2009-1/RJournal_2009-1_Mi+et+al.pdf