TruncatedNormal (version 2.3)

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"),
  B = 10000,
  check = TRUE,
  ...
)

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

B

number of replications for the (quasi)-Monte Carlo scheme

check

logical, if TRUE (default), check that the scale matrix sigma is positive definite and symmetric.

...

additional arguments, currently ignored.

Author

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)
if (FALSE) {
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)
}