rPseudoWishart {CholWishart} | R Documentation |
Generate n random matrices, distributed according
to the pseudo Wishart distribution with parameters Sigma
and
df
, W_p(Sigma, df), with sample size
df
less than the dimension p
.
Let X_i, i = 1, 2, ..., df be df
observations of a multivariate normal distribution with mean 0 and
covariance Sigma
. Then ∑ X_i X_i' is distributed as a pseudo
Wishart W_p(Sigma, df). Sometimes this is called a
singular Wishart distribution, however, that can be confused with the case
where Sigma itself is singular. If cases with a singular
Sigma are desired, this function cannot provide them.
rPseudoWishart(n, df, Sigma)
n |
integer sample size. |
df |
integer parameter, "degrees of freedom", should be less than the
dimension of |
Sigma |
positive definite (p * p) "scale" matrix, the matrix parameter of the distribution. |
a numeric array, say R
, of dimension p * p * n,
where each R[,,i]
is a realization of the pseudo Wishart distribution
W_p(Sigma, df).
Diaz-Garcia, Jose A, Ramon Gutierrez Jaimez, and Kanti V Mardia. 1997. “Wishart and Pseudo-Wishart Distributions and Some Applications to Shape Theory.” Journal of Multivariate Analysis 63 (1): 73–87. doi: 10.1006/jmva.1997.1689.
Uhlig, Harald. On Singular Wishart and Singular Multivariate Beta Distributions. Ann. Statist. 22 (1994), no. 1, 395–405. doi: 10.1214/aos/1176325375.
rWishart
, rInvWishart
,
and rGenInvWishart
set.seed(20181227) A<-rPseudoWishart(1L, 4L, 5.0*diag(5L))[,,1] # A should be singular eigen(A)$values