Distribution functions for matrix variate inverted t distributions

Source: R/matrixt.R

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

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

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

L

\(p \times p\) matrix specifying relations among the rows. By default, an identity matrix.

R

\(q \times q\) matrix specifying relations among the columns. By default, an identity matrix.

U

\(LL^T\) - \(p \times p\) positive definite matrix for rows, computed from \(L\) if not specified.

V

\(R^T R\) - \(q \times q\) 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 \(n\) \(p \times q\) matrices or a \(p \times q \times n\) 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

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))
#> [1] 193350.9