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

Description Usage Arguments Details Value References See Also Examples

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

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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)

`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.

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.

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.

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,

dmst, dfmmst

x <- seq(-2,4,length=21)
y <- 2*x+10
z <- x+cos(y)
mu <- c(1,12,2)
sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
dof <- 4
f  <- dmt(cbind(x,y,z), mu, sigma,dof)
## Not run:                       
p1 <- pmt(c(2,11,3), mu, sigma, dof)
p2 <- pmt(c(2,11,3), mu, sigma, dof, maxpts=10000, abseps=1e-8)

## End(Not run)

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$dof <- c(1, 2, 3)
obj$pro <- c(0.25, 0.25, 0.5)
dfmmt(matrix(c(1,2,5,6,2,4),3,2), obj$mu, obj$sigma, obj$dof, obj$pro)
dfmmt(c(1,2), known=obj)