pmvnorm function

Distribution function of the multivariate normal distribution for arbitrary limits

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.

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

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
• ...: additional arguments, currently ignored.

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))

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

Author(s)

Zdravko I. Botev, Leo Belzile (wrappers)