rdemmix: Simulate Data Using Mixture Models
In EMMIXskew: The EM Algorithm and Skew Mixture Distribution

Description Usage Arguments Details Value References See Also Examples

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

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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)

`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.

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.

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.

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.

rdmvn,rdmvt,rdmsn, rdmst.

#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)