TruncatedNormal: pmvnorm – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

pmvnorm

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"),
  log = FALSE
)

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
`log`	logical; if `TRUE`, probabilities and density are given on the log scale.

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.

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))

TruncatedNormal

Truncated Multivariate Normal and Student Distributions

v2.2

GPL-3

Authors

Zdravko Botev [aut] (<https://orcid.org/0000-0001-9054-3452>), Leo Belzile [aut, cre] (<https://orcid.org/0000-0002-9135-014X>)

Initial release

2020-05-16