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.

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)

rmvnorm_cpp(mean, Sigma, log = FALSE)

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

pmvnorm(x, mean, Sigma, abseps = 0.001)

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.
n	[integer(1)] The number of requested samples.

Details

pmvnorm() just 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.

Value

For dmvnorm(): The density value.

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

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)

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

oeli documentation built on Aug. 18, 2025, 5:24 p.m.