Skip to contents

Normal and t-mixture distributions

mixt.Rd

Random generation and density values from normal and t-mixture distributions.

Usage

dnorm.mixt(x, mus=0, sigmas=1, props=1)
rnorm.mixt(n=100, mus=0, sigmas=1, props=1, mixt.label=FALSE)
dmvnorm.mixt(x, mus, Sigmas, props=1, verbose=FALSE)
rmvnorm.mixt(n=100, mus=c(0,0), Sigmas=diag(2), props=1, mixt.label=FALSE)
rmvt.mixt(n=100, mus=c(0,0), Sigmas=diag(2), dfs=7, props=1)
dmvt.mixt(x, mus, Sigmas, dfs, props)
mvnorm.mixt.mode(mus, Sigmas, props=1, verbose=FALSE)

Arguments

n

number of random variates

x

matrix of quantiles

mus

(stacked) matrix of mean vectors (>1-d) or vector of means (1-d)

Sigmas

(stacked) matrix of variance matrices (>1-d)

sigmas

vector of standard deviations (1-d)

props

vector of mixing proportions

mixt.label

flag to output numeric label indicating mixture component. Default is FALSE.

verbose

flag to print out progress information. Default is FALSE.

dfs

vector of degrees of freedom

Value

Normal and t-mixture random vectors and density values.

Details

rmvnorm.mixt and dmvnorm.mixt are based on the rmvnorm and dmvnorm functions from the mvtnorm package. Likewise for rmvt.mixt and dmvt.mixt.

For the normal mixture densities, mvnorm.mixt.mode computes the local modes: these are usually very close but not exactly equal to the component means.

Examples

## univariate normal mixture
x <- rnorm.mixt(1000, mus=c(-1,1), sigmas=c(0.5, 0.5), props=c(1/2, 1/2))

## bivariate mixtures 
mus <- rbind(c(-1,0), c(1, 2/sqrt(3)), c(1,-2/sqrt(3)))
Sigmas <- 1/25*rbind(invvech(c(9, 63/10, 49/4)), invvech(c(9,0,49/4)), invvech(c(9,0,49/4)))
props <- c(3,3,1)/7
dfs <- c(7,3,2)
x <- rmvnorm.mixt(1000, mus=mus, Sigmas=Sigmas, props=props)
y <- rmvt.mixt(1000, mus=mus, Sigmas=Sigmas, dfs=dfs, props=props)

mvnorm.mixt.mode(mus=mus, Sigmas=Sigmas, props=props)
#>            [,1]         [,2]
#> [1,] -0.9975330  0.002125069
#> [2,]  0.9898321  1.153091638
#> [3,]  0.9999969 -1.119886815