TruncatedNormal: pmvt – R documentation

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

pmvt

Distribution function of the multivariate Student distribution for arbitrary limits

Description

This function computes the distribution function of a multivariate normal distribution vector for an arbitrary rectangular region [lb, ub]. pmvt 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

pmvt(
  mu,
  sigma,
  df,
  lb = -Inf,
  ub = Inf,
  type = c("mc", "qmc"),
  log = FALSE,
  B = 10000
)

Arguments

`mu`	vector of location parameters
`sigma`	scale matrix
`df`	degrees of freedom
`lb`	vector of lower truncation limits
`ub`	vector of upper truncation limits
`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.
`B`	number of replications for the (quasi)-Monte Carlo scheme

Author(s)

Matlab code by Zdravko I. Botev, R port by Leo Belzile

References

Z. I. Botev and P. L'Ecuyer (2015), Efficient probability estimation and simulation of the truncated multivariate Student-t distribution, Proceedings of the 2015 Winter Simulation Conference, pp. 380-391

Examples

d <- 15; nu <- 30;
l <- rep(2, d); u <- rep(Inf, d);
sigma <- 0.5 * matrix(1, d, d) + 0.5 * diag(1, d);
est <- pmvt(lb = l, ub = u, sigma = sigma, df = nu)
# mvtnorm::pmvt(lower = l, upper = u, df = nu, sigma = sigma)
## Not run: 
d <- 5
sigma <- solve(0.5 * diag(d) + matrix(0.5, d, d))
# mvtnorm::pmvt(lower = rep(-1,d), upper = rep(Inf, d), df = 10, sigma = sigma)[1]
pmvt(lb = rep(-1, d), ub = rep(Inf, d), sigma = sigma, df = 10)

## End(Not run)

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