# dfmmst: Multivariate skew t distribution In EMMIXuskew: Fitting Unrestricted Multivariate Skew t Mixture Models

## Description

The probability density function for the unrestricted multivariate skew t (MST) distribution and finite mixture of MSN and MST distributions

## Usage

 ```1 2 3``` ```dfmmst(dat, mu = NULL, sigma = NULL, delta = NULL, dof = NULL, pro = NULL, known = NULL, tmethod=1) dmst(dat, mu = NULL, sigma = NULL, delta = NULL, dof = 1, known = NULL, tmethod=1) ```

## 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 `dmst`, this is a numeric vector of length `p` representing the location parameter; for `dfmmst`, this is list of `g` numeric matrices each having `p` rows and `1` column containing the location parameter for each component. `sigma` for `dmst`, this is a numeric positive definite matrix with dimension `(p,p)` representing the scale parameter; for `dfmmst`, this is list of `g` numeric matrices containing the scale parameter for each component. `delta` for `dmst`, this is a numeric vector of length `p` representing the skewness parameter; for `dfmmst`, this is list of `g` numeric matrices each having `p` rows and `1` column containing the skewness parameter for each component. `dof` for `dmst`, this is a positive integer specifying the degrees of freedom; for `dfmmst`, this is numeric vector of length `g` representing the degrees of freedom for each component. `pro` the mixing proportions; for`dmst`, this is equal to `1`; for `dfmmst`, 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`. `tmethod` (optional) an integer indicating which method to use when computing t distribution function values. See `pmt` for details.

## Details

The function `dmst` computes the density value of a specified unrestricted multivariate skew t (MST) 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 `dfmmst` computes the density value for a specified mixture of MST distribution. Note that `dfmmst` expects at least `dof` is specified. Other missing parameters will take the default value described above. When `g=1`, `dfmmst` passes the call to `dmst`. Model parameters can be passed to `dmst` and `dfmmst` 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

`dmst` and `dfmmst` returns a numeric vector of density values

## References

Sahu S, Dey D, Branco M (2003). A New Class of Multivariate Skew Distributions with Applications to Bayesian Regression Models. The Canadian Journal of Statistics, 31, 129-150.

Lee S, McLachlan G (2011). On the fitting of mixtures of multivariate skew t-distributions via the EM algorithm. arXiv:1109.4706 [stat.ME]

Lee, S. and McLachlan, G.J. (2014) Finite mixtures of multivariate skew t-distributions: some recent and new results. Statistics and Computing, 24, 181-202.

## See Also

`rmst`, `rfmmst`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ``` dmst(c(1,2), mu=c(1,5), sigma=diag(2), delta=c(-3,1), dof=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(c(3,1.5), c(5,10), c(2,0)) obj\$dof <- c(1, 2, 3) obj\$pro <- c(0.25, 0.25, 0.5) dfmmst(matrix(c(1,2,5,6,2,4),3,2), obj\$mu, obj\$sigma, obj\$delta, obj\$dof, obj\$pro) dfmmst(c(1,2), known=obj) ```

EMMIXuskew documentation built on May 29, 2017, 11:25 p.m.