Mixture of normal distributions

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, log = FALSE)

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

rmixnorm_cpp(mean, Sigma, proportions, log = FALSE)

dmixnorm(x, mean, Sigma, proportions, log = FALSE)

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

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

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.

log

[logical(1)]
For dmixnorm(), return the logarithm of the density value?

For rmixnorm(), return the exponential of the draw, which is a draw from the mixture of log-normal distributions?

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.

Value

For dmixnorm(): The density value.

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

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 pmvnorm(), which is exact for p <= 3 and approximates the probability by the method selected in method otherwise.

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
dmixnorm(
  x = x, mean = mean, Sigma = Sigma, proportions = proportions, log = TRUE
)
#> [1] -2.422142

# compute CDF
pmixnorm(x = x, mean = mean, Sigma = Sigma, proportions = proportions)
#> [1] 0.5705027

# compute rectangle probability
pmixnorm(
  x = x, mean = mean, Sigma = Sigma, proportions = proportions, lower = -1
)
#> [1] 0.1165162

# sample
rmixnorm(n = 3, mean = mean, Sigma = Sigma, proportions = proportions)
#>            [,1]      [,2]
#> [1,] -1.3107073 -1.520797
#> [2,] -0.7407926 -1.594475
#> [3,]  1.6442855 -1.360091