pmvnorm: Distribution function of the multivariate normal distribution...

In lbelzile/TruncatedNormal: Truncated Multivariate Normal and Student Distributions

Distribution function of the multivariate normal distribution for arbitrary limits

Description

This function computes the distribution function of a multivariate normal distribution vector for an arbitrary rectangular region [lb, ub]. pmvnorm computes an estimate and the value is returned along with a relative error and a deterministic upper bound of the distribution function of the multivariate normal distribution. Infinite values for vectors u and l are accepted. The Monte Carlo method uses sample size n: the larger the sample size, the smaller the relative error of the estimator.

Usage

pmvnorm(
  mu,
  sigma,
  lb = -Inf,
  ub = Inf,
  B = 10000,
  type = c("mc", "qmc"),
  check = TRUE,
  ...
)

Arguments

mu	vector of location parameters
sigma	covariance matrix
lb	vector of lower truncation limits
ub	vector of upper truncation limits
B	number of replications for the (quasi)-Monte Carlo scheme
type	string, either of mc or qmc for Monte Carlo and quasi Monte Carlo, respectively
check	logical; if TRUE (default), the code checks that the scale matrix sigma is positive definite and symmetric
...	additional arguments, currently ignored.

Author(s)

Zdravko I. Botev, Leo Belzile (wrappers)

References

Z. I. Botev (2017), The normal law under linear restrictions: simulation and estimation via minimax tilting, Journal of the Royal Statistical Society, Series B, 79 (1), pp. 1–24.

See Also

pmvnorm

Examples

#From mvtnorm
mean <- rep(0, 5)
lower <- rep(-1, 5)
upper <- rep(3, 5)
corr <- matrix(0.5, 5, 5) + diag(0.5, 5)
prob <- pmvnorm(lb = lower, ub = upper, mu = mean, sigma = corr)
stopifnot(pmvnorm(lb = -Inf, ub = 3, mu = 0, sigma = 1) == pnorm(3))

lbelzile/TruncatedNormal documentation built on March 4, 2024, 5:50 p.m.