rmatrixinvt {MixMatrix}R Documentation

Distribution functions for matrix variate inverted t distributions

Description

Generate random samples from the inverted matrix variate t distribution or compute densities.

Usage

rmatrixinvt(n, df, mean, L = diag(dim(as.matrix(mean))[1]),
  R = diag(dim(as.matrix(mean))[2]), U = L %*% t(L), V = t(R) %*%
  R, list = FALSE, array = NULL)

dmatrixinvt(x, df, mean = matrix(0, p, n), L = diag(p), R = diag(n),
  U = L %*% t(L), V = t(R) %*% R, log = FALSE)

Arguments

n

number of observations for generation

df

degrees of freedom (>0, may be non-integer), df = 0, Inf is allowed and will return a normal distribution.

mean

p * q This is really a 'shift' rather than a mean, though the expected value will be equal to this if df > 2

L

p * p matrix specifying relations among the rows. By default, an identity matrix.

R

q * q matrix specifying relations among the columns. By default, an identity matrix.

U

LL^T - p * p positive definite matrix for rows, computed from L if not specified.

V

R^T R - q * q positive definite matrix for columns, computed from R if not specified.

list

Defaults to FALSE . If this is TRUE , then the output will be a list of matrices.

array

If n = 1 and this is not specified and list is FALSE , the function will return a matrix containing the one observation. If n > 1 , should be the opposite of list . If list is TRUE , this will be ignored.

x

quantile for density

log

logical; in dmatrixt, if TRUE, probabilities p are given as log(p).

Value

rmatrixinvt returns either a list of n p * q matrices or a p * q * n array.

dmatrixinvt returns the density at x.

References

Gupta, Arjun K, and Daya K Nagar. 1999. Matrix Variate Distributions. Vol. 104. CRC Press. ISBN:978-1584880462

Dickey, James M. 1967. “Matricvariate Generalizations of the Multivariate t Distribution and the Inverted Multivariate t Distribution.” Ann. Math. Statist. 38 (2): 511–18. doi: 10.1214/aoms/1177698967

See Also

rmatrixnorm, rmatrixt, and Distributions.

Examples

# an example of drawing from the distribution and computing the density.
A<-rmatrixinvt(n = 2, df = 10, diag(4))
dmatrixinvt(A[,,1], df = 10, mean = diag(4))

[Package MixMatrix version 0.2.2 Index]