# rmatrixinvt: Distribution functions for matrix variate inverted t... In MixMatrix: Classification with Matrix Variate Normal and t Distributions

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```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

`rmatrixnorm()`, `rmatrixt()`, and `stats::Distributions()`.
 ```1 2 3``` ```# 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)) ```