EMMIXcskew (version 0.9-5)

rfmcfust: Simulation of Mixture Data

Description

Generate random sample from a specified mixture of multivariate canonical fundamental skew t distribution

Usage

rfmcfust(g, n, mu, sigma, delta, dof=rep(10,g), pro=rep(1/g,g), known=NULL) 
rcfust(n=1, mu = NULL, sigma=NULL, delta=NULL, dof=1, known=NULL)

Arguments

g

a scalar specifying the number of components in the mixture model

n

either a positive integer specifying the total number of points to be generated or a vector (of length g) of positive integers specifying the number of points to be generated in each component.

mu

for rcfust, this is a numeric vector of length p representing the location parameter; for rfmcfust, this is list of g numeric matrices each having p rows and 1 column containing the location parameter for each component.

sigma

for rcfust, this is a numeric positive definite matrix with dimension (p,p) representing the scale parameter; for rfmcfust, this is list of g numeric matrices containing the scale parameter for each component.

delta

for rcfust, this is a numeric matrix of size p by q representing the skewness matrix; for rfmcfust, this is list of g numeric matrices each having p rows and q column containing the skewness parameter for each component.

dof

for rcfust, this is a positive integer specifying the degrees of freedom; for rfmcfust, this is numeric vector of length g representing the degrees of freedom for each component.

pro

the mixing proportions; for rcfust, this is equal to 1; for rfmcfust, this is vector of length of g specifying the mixing proportions for each component.

known

a list containing the parameters of the model. If specified, it overwrites the values of mu, sigma, delta, dof and pro.

Value

rcfust returns an n by p numeric matrix of generated data. rfmcfust returns an n by p+1 numeric matrix of genertaed data. The first p gives the coordinates of the generated data. The last column specifies which component each data point is generated from.

Details

rcfust generates a sample n multivariate CFUST observations. rfmcfust generates a mixture of CFUST observation. Note that model parameters can be passed to rcfust and rfmcfust through the argument known or listed as individual arguments. If both methods of input were used, the parameters specified in known will be used.

References

Lee S.X. and McLachlan, G.J. (2016). Finite mixtures of canonical fundamental skew t-distributions: the unification of the restricted and unrestricted skew t-mixture models. Statistics and Computing 26, 573-589.

Lee S.X. and McLachlan, G.J. (2017). EMMIXcskew: An R Package for the Fitting of a Mixture of Canonical Fundamental Skew t-Distributions. Journal of Statistical Software 83(3), 1-32. URL 10.18637/jss.v083.i03.

See Also

dcfust, dfmcfust

Examples

# NOT RUN {
##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.
rcfust(10,c(1,2),diag(2),matrix(c(2,1,1,2),2,2),4)

obj <- list()
obj$mu <- list(c(17,19), c(5,22), c(6,10))
obj$sigma <- list(diag(2), matrix(c(2,0,0,1),2), matrix(c(3,7,7,24),2))
obj$delta <- list(matrix(c(3,0,2,1.5),2,2), matrix(c(5,0,0,10),2,2), matrix(c(2,0,5,0),2,2))
obj$dof <- c(1, 2, 3)
obj$pro <- c(0.25, 0.25, 0.5)
rfmcfust(3, 100, known=obj)

# }