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

## Description

The probability density function and distribution function for the multivariate Student t distribution and mixtures of multivariate t distribution

## Usage

 1 2 3 dmt(dat, mu, sigma, dof = Inf, log = FALSE) pmt(dat, mu=rep(0,length(dat)), sigma=diag(length(dat)), dof=Inf, method=1, ...) dfmmt(dat, mu = NULL, sigma = NULL, dof = NULL, pro = NULL, known = NULL)

## Arguments

 dat for dmt, this is the data matrix giving the coordinates of the point(s) where the density is evaluated. for pmt, this is either a vector of length p. Currently, only p up to 20 dimensions is supported. mu a numeric vector of length p representing the location parameter; sigma a numeric positive definite matrix with dimension (p,p) representing the scale parameter dof a positive real number specifying the degrees of freedom. If tmethod=1, dof will be rounded to the nearest integer. pro the mixing proportions; for dmt, this is equal to 1; for dfmmt, this is vector of length of g specifying the mixing proportions for each component. log a logical value; if TRUE, the logarithm of the density is computed ... parameters passed to sadmvt, among maxpts, absrel, releps known a list containing the parameters of the model. If specified, it overwrites the values of mu, sigma, dof and pro. method the method to use for computation of t distribution function. See description.

## Details

There are three options in pmt for computing multivariate t distribution function values. method=1 uses requires dof to be an integer. This provide interfaces to the Fortran-77 routines by Alan Genz. This is the fastest method of the three options avilable. method=2 uses linear interpolation technique to calculate t distribution function values for a positive real dof. This method requires double the time of method 1. method=3 uses a method described in Genz and Bretz (2002). This is the more accurate method for a non-integer dof, but more computationally intensive than the other two methods.

## Value

The function dmt computes the density value of a specified multivariate t distribution. pmt computes the distribution value for a SINGLE point. dfmmt returns a numeric vector of mixture density values.

## References

Genz, A.: Fortran code in files mvt.f and mvtdstpack.f available at http://www.math.wsu.edu/math/faculty/genz/software/

Genz, A. and Bretz, F. (2002). Comparison of Methods for the Numerical Computation of Multivariate t Probabilities. J. of Comput. Graph. Stat., 11:950-971,