dmixnorm: Mixture of normal distributions

In oeli: Some Utilities for Developing Data Science Software

Mixture of normal distributions

Description

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

The function pmixnorm() computes the cumulative distribution function of a mixture of multivariate normal distribution.

The function rmixnorm() samples from a mixture of multivariate normal distribution.

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

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

Usage

dmixnorm_cpp(x, mean, Sigma, proportions)

pmixnorm_cpp(x, mean, Sigma, proportions, abseps = 0.001)

rmixnorm_cpp(mean, Sigma, proportions)

dmixnorm(x, mean, Sigma, proportions)

pmixnorm(x, mean, Sigma, proportions, abseps = 0.001)

rmixnorm(n = 1, mean, Sigma, proportions)

Arguments

x	[numeric(p)] A quantile vector of length p, where p is the dimension.
mean	[matrix(nrow = p, ncol = c)] The mean vectors for each component in columns.
Sigma	[matrix(nrow = p^2, ncol = c)] The vectorized covariance matrices for each component in columns.
proportions	[numeric(c)] The non-negative mixing proportions for each components. If proportions do not sum to unity, they are rescaled to do so.
abseps	[numeric(1)] The absolute error tolerance.
n	[integer(1)] The number of requested samples.

Details

pmixnorm() is based on 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 dmixnorm(): The density value.

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

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

See Also

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

Examples

x <- c(0, 0)
mean <- matrix(c(-1, -1, 0, 0), ncol = 2)
Sigma <- matrix(c(diag(2), diag(2)), ncol = 2)
proportions <- c(0.7, 0.3)

# compute density
dmixnorm(x = x, mean = mean, Sigma = Sigma, proportions = proportions)

# compute CDF
pmixnorm(x = x, mean = mean, Sigma = Sigma, proportions = proportions)

# sample
rmixnorm(n = 3, mean = mean, Sigma = Sigma, proportions = proportions)

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