rmatrixt {MixMatrix} | R Documentation |
Density and random generation for the matrix variate t distribution.
rmatrixt(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, force = FALSE) dmatrixt(x, df, mean = matrix(0, p, n), L = diag(p), R = diag(n), U = L %*% t(L), V = t(R) %*% R, log = FALSE)
n |
number of observations for generation |
df |
degrees of freedom (>0, may be non-integer),
|
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 |
array |
If n = 1 and this is not specified and |
force |
In |
x |
quantile for density |
log |
logical; in |
The matrix t-distribution is parameterized slightly
differently from the univariate and multivariate t-distributions
- the variance is scaled by a factor of 1/df
.
In this parameterization, the variance for a 1 * 1 matrix
variate t-distributed random variable with identity variance matrices
is 1/(df-2) instead of df/(df-2). A Central Limit Theorem
for the matrix variate T is then that as df
goes to
infinity, MVT(0, df, I_p, df*I_q) converges to
MVN(0,I_p,I_q).
rmatrixt
returns either a list of n
p * q matrices or a p * q * n
array.
dmatrixt
returns the density at x
.
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
,
rmatrixinvt
,rt
and Distributions
.
set.seed(20180202) # random matrix with df = 10 and the given mean and L matrix rmatrixt(n=1,df=10,mean=matrix(c(100,0,-100,0,25,-1000),nrow=2), L=matrix(c(2,1,0,.1),nrow=2),list=FALSE) # comparing 1-D distribution of t to matrix summary(rt(n=100,df=10)) summary(rmatrixt(n=100,df=10,matrix(0))) # demonstrating equivalence of 1x1 matrix t to usual t set.seed(20180204) x = rmatrixt(n=1,mean=matrix(0),df=1) dt(x,1) dmatrixt(x,df=1)