Mvt {mvtnorm} | R Documentation |
These functions provide information about the multivariate t
distribution with non-centrality parameter (or mode) delta
,
scale matrix sigma
and degrees of freedom df
.
dmvt
gives the density and rmvt
generates random deviates.
rmvt(n, sigma = diag(2), df = 1, delta = rep(0, nrow(sigma)), type = c("shifted", "Kshirsagar"), ...) dmvt(x, delta, sigma, df = 1, log = TRUE, type = "shifted")
x |
Vector or matrix of quantiles. If |
n |
Number of observations. |
delta |
the vector of noncentrality parameters of length n, for
|
sigma |
Correlation matrix, default is |
df |
degree of freedom as integer. |
log |
Logical; if |
type |
type of the noncentral multivariate t distribution
to be computed. |
... |
additional arguments to |
For type = "shifted" the following density is implemented
c(1+(x-δ)'S^{-1}(x-δ)/ν)^{-(ν+m)/2},
where
c = Γ((ν+m)/2)/((π ν)^{m/2}Γ(ν/2)|S|^{1/2}),
here S is a positive definite symmetric matrix (which might be the correlation or the scale matrix), delta is the non-centrality vector and ν are the degrees of freedom.
dmvt(x=c(0,0), sigma = diag(2)) x <- rmvt(n=100, sigma = diag(2), df = 3) plot(x)