EMMIXskew (version 1.0.3)

rdemmix: Simulate Data Using Mixture Models

Description

Generate random number from specified mixture models, including univariate and multivariate Normal distribution, t-distribution, Skew Normal distribution, and Skew t-distribution.

Usage

rdemmix(nvect,p,g,distr,    mu,sigma,dof=NULL,delta=NULL)
rdemmix2(n,   p,g,distr,pro,mu,sigma,dof=NULL,delta=NULL)
rdemmix3(n,   p,g,distr,pro,mu,sigma,dof=NULL,delta=NULL)

Arguments

nvect

A vector of how many points in each cluster,c(n1,n2,..,ng)

n

The total number of points

p

Dimension of data

g

The number of clusters

distr

A three letter string indicating the distribution type

pro

A vector of mixing proportions, see Details.

mu

A numeric matrix with each column corresponding to the mean, see Details.

sigma

An array of dimension (p,p,g) with first two dimension corresponding covariance matrix of each component, see Details.

dof

A vector of degrees of freedom for each component, see Details.

delta

A p by g matrix with each column corresponding to a skew parameter vector, see Details.

Value

both rdemmix and rdemmix2 return an n by p numeric matrix of generated data;

rdemmix3 gives a list with components data, the generated data, and cluster, the clustering of data.

Details

The distribution type, determined by the distr parameter, which may take any one of the following values: "mvn" for a multivariate normal, "mvt" for a multivariate t-distribution, "msn" for a multivariate skew normal distribution and "mst" for a multivariate skew t-distribution. pro, a numeric vector of the mixing proportion of each component; mu, a p by g matrix with each column as its corresponding mean; sigma, a three dimensional p by p by g array with its jth component matrix (p,p,j) as the covariance matrix for jth component of mixture models; dof, a vector of degrees of freedom for each component; delta, a p by g matrix with its columns corresponding to skew parameter vectors.

References

McLachlan G.J. and Krishnan T. (2008). The EM Algorithm and Extensions (2nd). New Jersay: Wiley.

McLachlan G.J. and Peel D. (2000). Finite Mixture Models. New York: Wiley.

See Also

rdmvn,rdmvt,rdmsn, rdmst.

Examples

# NOT RUN {
#specify the dimension of data, and number of clusters
#the number of observations in each cluster
n1=300;n2=300;n3=400;
nn<-c(n1,n2,n3)

p=2
g=3



#specify the distribution
distr <- "mvn"

#specify mean and covariance matrix for each component

sigma<-array(0,c(2,2,3))
for(h in 2:3) sigma[,,h]<-diag(2)
sigma[,,1]<-cbind( c(1,-0.1),c(-0.1,1))
mu  <- cbind(c(4,-4),c(3.5,4),c( 0, 0))

#reset the random seed 
set.seed(111) 
#generate the dataset
dat <- rdemmix(nn,p,g,distr,    mu,sigma)



# alternatively one can use
pro   <- c(0.3,0.3,0.4)
n=1000
set.seed(111)
dat <- rdemmix2(n,p,g,distr,pro,mu,sigma)
plot(dat)

# and 

set.seed(111)
dobj <- rdemmix3(n,p,g,distr,pro,mu,sigma)
plot(dobj$data)


#other distributions such as "mvt","msn", and "mst".

#t-distributions

dof    <- c(3,5,5)
dat <- rdemmix2(n,p,g,"mvt",pro,mu,sigma,dof)
plot(dat)

#Skew Normal distribution
delta <- cbind(c(3,3),c(1,5),c(-3,1))
dat <- rdemmix2(n,p,g,"msn",pro,mu,sigma,delta=delta)
plot(dat)


#Skew t-distribution
dat <- rdemmix2(n,p,g,"mst",pro,mu,sigma,dof,delta)
plot(dat)



# }