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 lengthp, wherepis 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.
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.
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.
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)
#> [1] 0.08873136
# compute CDF
pmixnorm(x = x, mean = mean, Sigma = Sigma, proportions = proportions)
#> [1] 0.5705027
# sample
rmixnorm(n = 3, mean = mean, Sigma = Sigma, proportions = proportions)
#> [,1] [,2]
#> [1,] -0.8200754 -0.1215489
#> [2,] -2.9877176 1.0323998
#> [3,] -0.1631780 -0.6575572