mvtNormQuasiMonteCarlo: Multivariate normal distribution function

In mvPot: Multivariate Peaks-over-Threshold Modelling for Spatial Extreme Events

Multivariate normal distribution function

Description

Estimate the multivariate distribution function with quasi-Monte Carlo method.

Usage

mvtNormQuasiMonteCarlo(p, upperBound, cov, genVec, ...)

Arguments

p	Number of samples used for quasi-Monte Carlo estimation. Must be a prime number.
upperBound	Vector of probabilities, i.e., the upper bound of the integral.
cov	Covariance matrix of the multivariate normal distribution. Must be positive semi-definite. WARNING: for performance in high-dimensions, no check is performed on the matrix. It is the user responsibility to ensure that the matrix is positive semi-definite.
genVec	Generating vector for the quasi-Monte Carlo procedure. Can be computed using genVecQMC.
...	Additional arguments passed to Cpp routine.

Details

The function uses a quasi-Monte Carlo procedure based on randomly shifted lattice rules to estimate the distribution function a multivariate normal distribution as described in Genz and Bretz (2009) on page 50.

Value

A named vector with components estimate estimate of the distribution function along error, 3 times the empirical Monte Carlo standard error over the nrep replications.

Source

Adapted from the QSILATMVNV by A. Genz (2013)

References

Genz, A. and Bretz, F. (2009). Computations of Multivariate Normal and t Probabilities, volume 105. Springer: Dordrecht.

Examples

#Define locations
loc <- expand.grid(1:4, 1:4)
ref <- sample.int(16, 1)

#Compute variogram matrix
variogramMatrix <- ((sqrt((outer(loc[,1],loc[,1],"-"))^2 +
(outer(loc[,2],loc[,2],"-"))^2)) / 2)^(1.5)

#Define an upper boud
upperBound <- variogramMatrix[-ref,ref]

#Compute covariance matrix
cov <-  (variogramMatrix[-ref,ref]%*%t(matrix(1, (nrow(loc) - 1), 1)) +
t(variogramMatrix[ref,-ref]%*%t(matrix(1, (nrow(loc) - 1), 1))) -
variogramMatrix[-ref,-ref])

#Compute generating vector
p <- 499
latticeRule <- genVecQMC(p, (nrow(loc) - 1))

#Estimate the multivariate distribution function
mvtNormQuasiMonteCarlo(latticeRule$primeP, upperBound, cov, latticeRule$genVec)

mvPot documentation built on April 4, 2025, 5:28 a.m.