| Title: | Multivariate Probabilities of Scale Mixtures of Multivariate Normal Distributions via the Genz and Bretz (2002) QRSVN Method |
| Version: | 0.0.6 |
| Description: | Generates multivariate subgaussian stable probabilities using the QRSVN algorithm as detailed in Genz and Bretz (2002) <doi:10.1198/106186002394> but by sampling positive stable variates not chi/sqrt(nu). |
| Depends: | R (≥ 3.4.0) |
| License: | LGPL-2.1 | LGPL-3 [expanded from: LGPL (≥ 2.1)] |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.1 |
| URL: | https://github.com/swihart/mvgb |
| BugReports: | https://github.com/swihart/mvgb/issues |
| NeedsCompilation: | yes |
| Packaged: | 2024-10-03 18:22:32 UTC; bruce |
| Author: | Alan Genz [aut] (wrote mvtdstpack.f),
Bruce Swihart 
[aut, cre] |
| Maintainer: | Bruce Swihart <bruce.swihart@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2024-10-03 23:10:10 UTC |
Multivariate Probabilities of Scale Mixtures of Multivariate Normal Distributions
Description
The QRVSN algorithm is used in a broader context: using the Genz and Bretz (2002) algorithm to calculate multivariate distribution probabilities.
Multivariate Subgaussian Stable Distribution
pmvss – multivariate subgaussian stable distribution probabilities
Author(s)
Maintainer: Bruce Swihart bruce.swihart@gmail.com (ORCID)
Authors:
Alan Genz (wrote mvtdstpack.f)
See Also
Useful links:
Multivariate Subgaussian Stable Distribution Probabilities (via positive stable variates)
Description
Computes the the distribution function of the multivariate subgaussian stable
distribution for arbitrary limits, alpha,
shape matrices, and ___location vectors.
This function is unlike mvtnorm::pmvt in two ways:
The QRVSN method is used for every dimension
n(including bivariate and trivariate),The QRVSN method on positive stable variates, not chi/sqrt(nu).
Usage
pmvss(
lower,
upper,
alpha,
Q,
delta = rep(0, NROW(Q)),
maxpts = 25000,
abseps = 0.001,
releps = 0
)
Arguments
lower |
lower bounds of integration must be length n, finite |
upper |
upper bounds of integration must be length n, finite |
alpha |
real number between 0 and 2 that cannot have more than 6 digits precision. 0.123456 is okay; 0.1234567 is not. Thus alpha in [0.000001, 1.999999]. |
Q |
shape matrix |
delta |
___location vector must have length equal to the number of rows of Q. Defaults to the 0 vector. |
maxpts |
(description from FORTRAN code) INTEGER, maximum number of function values allowed. This parameter can be used to limit the time. A sensible strategy is to start with MAXPTS = 1000*N, and then increase MAXPTS if ERROR is too large. (description from mvtnorm::GenzBretz) 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 |
releps |
relative error tolerance as double. |
Value
Returns the variables from the MVTDST function (QRVSN algorithm):
N INTEGER, the number of variables.
NU INTEGER, the number of degrees of freedom.
If NU < 1, then an MVN probability is computed.
LOWER DOUBLE PRECISION, array of lower integration limits.
UPPER DOUBLE PRECISION, array of upper integration limits.
INFIN INTEGER, array of integration limits flags:
if INFIN(I) < 0, Ith limits are (-infinity, infinity);
if INFIN(I) = 0, Ith limits are (-infinity, UPPER(I)];
if INFIN(I) = 1, Ith limits are [LOWER(I), infinity);
if INFIN(I) = 2, Ith limits are [LOWER(I), UPPER(I)].
CORREL DOUBLE PRECISION, array of correlation coefficients;
the correlation coefficient in row I column J of the
correlation matrix should be stored in
CORREL( J + ((I-2)*(I-1))/2 ), for J < I.
The correlation matrix must be positive semi-definite.
DELTA DOUBLE PRECISION, array of non-centrality parameters.
MAXPTS INTEGER, maximum number of function values allowed. This
parameter can be used to limit the time. A sensible
strategy is to start with MAXPTS = 1000*N, and then
increase MAXPTS if ERROR is too large.
ABSEPS DOUBLE PRECISION absolute error tolerance.
RELEPS DOUBLE PRECISION relative error tolerance.
error DOUBLE PRECISION estimated absolute error,
with 99% confidence level.
value DOUBLE PRECISION estimated value for the integral
inform INTEGER, termination status parameter:
if INFORM = 0, normal completion with ERROR < EPS;
if INFORM = 1, completion with ERROR > EPS and MAXPTS
function values used; increase MAXPTS to
decrease ERROR;
if INFORM = 2, N > 1000 or N < 1.
if INFORM = 3, correlation matrix not positive semi-definite.
RND ignore; this initializes RNG
References
Genz, A. and Bretz, F. (2002), Methods for the computation of multivariate t-probabilities. Journal of Computational and Graphical Statistics, 11, 950–971.
http://www.math.wsu.edu/faculty/genz/homepage
http://www.math.wsu.edu/faculty/genz/software/fort77/mvtdstpack.f
Examples
Q = structure(c(1, 0.85, 0.85, 0.85, 0.85,
0.85, 1 , 0.85, 0.85, 0.85,
0.85, 0.85 , 1 , 0.85, 0.85,
0.85, 0.85 , 0.85 , 1 , 0.85,
0.85, 0.85 , 0.85 , 0.85 , 1 ),
.Dim = c(5L,5L))
## default maxpts=25000 doesn't finish with error < abseps
mvgb::pmvss(lower=rep(-1,5),
upper=rep(1,5),
alpha=1,
Q=Q,
maxpts=25000)[c("value","inform","error")]
## increase maxpts to get inform value 0 (that is, error < abseps)
mvgb::pmvss(lower=rep(-1,5),
upper=rep(1,5),
alpha=1,
Q=Q,
maxpts=25000*350)[c("value","inform","error")]
set.seed(10)
shape_matrix <- structure(c(1, 0.9, 0.9, 0.9, 0.9, 0.9, 1, 0.9, 0.9, 0.9, 0.9,
0.9, 1, 0.9, 0.9, 0.9, 0.9, 0.9, 1, 0.9, 0.9, 0.9, 0.9, 0.9,
1), .Dim = c(5L, 5L))
mvgb::pmvss(lower=rep(-2,5),
upper=rep(2,5),
alpha=1.7,
Q=shape_matrix,
delta=rep(0,5),
maxpts=25000*30)[c("value","inform","error")]