dfmcfust: Multivariate canonical fundamental skew t-distribution

In EMMIXcskew: Fitting Mixtures of CFUST Distributions

Description

The probability density function for the multivariate canonical fundamental skew t (CFUST) distribution and finite mixture of CFUST distributions

Usage

dfmcfust(dat, mu=NULL, sigma=NULL, delta=NULL, dof=NULL, pro=NULL, known=NULL)
dcfust(dat, mu=NULL, sigma=NULL, delta=NULL, dof=1, known=NULL)

Arguments

dat	the data matrix giving the coordinates of the point(s) where the density is evaluated. This is either a vector of length p or a matrix with p columns.
mu	for dcfust, this is a numeric vector of length p representing the location parameter; for dfmcfust, this is list of g numeric matrices each having p rows and 1 column containing the location parameter for each component.
sigma	for dcfust, this is a numeric positive definite matrix with dimension (p,p) representing the scale parameter; for dfmcfust, this is list of g numeric matrices containing the scale parameter for each component.
delta	for dcfust, 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 dcfust, this is a positive integer specifying the degrees of freedom; for dfmcfust, this is numeric vector of length g representing the degrees of freedom for each component.
pro	the mixing proportions; fordcfust, this is equal to 1; for dfmcfust, 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.

Details

The function dcfust computes the density value of a specified multivariate canonical fundamental skew t (CFUST) distribution. If any model parameters are not specified, their default values are used: mu and delta are zero vectors, sigma is the identity matrix, and dof is 1.

The function dfmcfust computes the density value for a specified mixture of MST distribution. Note that dfmcfust expects at least dof is specified. Other missing parameters will take the default value described above. When g=1, dfmcfust passes the call to dcfust. Model parameters can be passed to dcfust and dfmcfust through the argument known or listed as individual arguments. If both methods of input were used, the parameters specified in known will be used.

Value

dcfust and dfmcfust returns a numeric vector of density values

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

rcfust, rfmcfust

Examples

           
dcfust(c(1,2), mu=c(1,5), sigma=diag(2), delta=matrix(c(-3,1,1,1),2,2), dof=4)

EMMIXcskew documentation built on May 2, 2019, 6:59 a.m.