dmvnorm: Multivariate normal distribution

In oeli: Some Utilities for Developing Data Science Software

Multivariate normal distribution

Description

The function dmvnorm() computes the density of a multivariate normal distribution.

The function pmvnorm() computes the cumulative distribution function of a multivariate normal distribution, or the probability of a rectangle if lower is specified.

The function rmvnorm() samples from a multivariate normal distribution.

The functions with suffix ⁠_cpp⁠ perform no input checks, hence are faster.

The univariate normal distribution is available as the special case p = 1.

Usage

dmvnorm_cpp(x, mean, Sigma, log = FALSE)

pmvnorm_cpp(
  x,
  mean,
  Sigma,
  abseps = 0.001,
  lower = NULL,
  method = "genz",
  draws = 500L
)

rmvnorm_cpp(mean, Sigma, log = FALSE)

dmvnorm(x, mean, Sigma, log = FALSE)

pmvnorm(
  x,
  mean,
  Sigma,
  abseps = 0.001,
  lower = NULL,
  method = "genz",
  draws = 500
)

rmvnorm(n = 1, mean, Sigma, log = FALSE)

Arguments

x	[numeric()] A quantile vector of length p.
mean	[numeric()] The mean vector of length p. For the functions without suffix ⁠_cpp⁠, it can also be of length 1 for convenience, then rep(mean, p) is considered.
Sigma	[matrix()] The covariance matrix of dimension p. For rmvnorm(), arbitrary dimensions (i.e., full rows and corresponding columns) of Sigma can be 0. For the functions without suffix ⁠_cpp⁠ and if p = 1, it can also be a single numeric for convenience. Note that Sigma is this case is a variance, which is a different format than in stats::dnorm() or stats::rnorm, which require a standard deviation.
log	[logical(1)] Consider the log-normal distribution?
abseps	[numeric(1)] The absolute error tolerance for method = "genz".
lower	[numeric() | NULL] Optionally lower limits of length p, where NULL corresponds to -Inf. For the functions without suffix ⁠_cpp⁠, it can also be of length 1 for convenience, then rep(lower, p) is considered.
method	[character(1)] Either "genz" or "ghk", see the details.
draws	[integer(1)] The number of Halton points for method = "ghk".
n	[integer(1)] The number of requested samples.

Details

For p <= 3, pmvnorm() computes the probability exactly: the bivariate case uses the algorithm of Genz (2004) and the trivariate case integrates the bivariate probability conditional on the third component.

For p > 3, the argument method selects the approximation:

• "genz" calls mvtnorm::pmvnorm with the randomized Quasi-Monte-Carlo procedure by Genz and Bretz. The argument abseps controls the accuracy of the Gaussian integral approximation.

• "ghk" uses the Geweke-Hajivassiliou-Keane simulator on draws quasi-random Halton points. The result is deterministic and smooth in x, mean, and Sigma, which makes it suitable for likelihood evaluations, and its accuracy increases with draws.

Value

For dmvnorm(): The density value.

For pmvnorm(): The value of the distribution function or the rectangle probability.

For rmvnorm(): If n = 1 a vector of length p (note that it is a column vector for rmvnorm_cpp()), else a matrix of dimension n times p with samples as rows.

See Also

Other simulation helpers: Simulator, correlated_regressors(), ddirichlet_cpp(), dmixnorm_cpp(), dtnorm_cpp(), dwishart_cpp(), gaussian_tv(), simulate_markov_chain()

Examples

x <- c(0, 0)
mean <- c(0, 0)
Sigma <- diag(2)

# compute density
dmvnorm(x = x, mean = mean, Sigma = Sigma)
dmvnorm(x = x, mean = mean, Sigma = Sigma, log = TRUE)

# compute CDF
pmvnorm(x = x, mean = mean, Sigma = Sigma)

# compute rectangle probability
pmvnorm(x = x, mean = mean, Sigma = Sigma, lower = -1)

# simulate in higher dimensions
pmvnorm(x = rep(0, 5), mean = 0, Sigma = diag(5), method = "ghk")

# sample
rmvnorm(n = 3, mean = mean, Sigma = Sigma)
rmvnorm(mean = mean, Sigma = Sigma, log = TRUE)

oeli documentation built on Sept. 4, 2026, 5:07 p.m.