Description Usage Arguments Details Value Author(s) References See Also Examples
Evaluate the density of a multivariate Student t distribution.
1 2 3 
x 
(n, d) 
df 
degrees of freedom (positive real number or 
loc 
location vector of dimension d (the number of columns
of 
scale 
covariance matrix of dimension (d, d). 
factor 
factorization matrix of the covariance matrix

log 

Internally used is factor
, so scale
is not required
to be provided if factor
is given.
The default factorization used is the Cholesky decomposition.
To this end, scale
needs to have full rank.
dStudent()
returns an nvector
with the
density values (default) or logdensity values (if log
)
of the multivariate Student t distribution with df
degrees of freedom, location vector loc
and scale matrix
scale
(a covariance matrix).
Marius Hofert
McNeil, A. J., Frey, R., and Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques, Tools. Princeton University Press.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  ## Generate a random correlation matrix in three dimensions
d < 3
set.seed(271)
A < matrix(runif(d * d), ncol = d)
P < cov2cor(A %*% t(A))
## Evaluate t_{3.5} density
df < 3.5
x < matrix(1:12/12, ncol = d) # evaluation points
dt < dStudent(x, df = df, scale = P)
stopifnot(all.equal(dt, c(0.013266542, 0.011967156, 0.010760575, 0.009648682),
tol = 1e7))
## Evaluate normal density
dn < dStudent(x, df = Inf, scale = P)
stopifnot(all.equal(dn, c(0.013083858, 0.011141923, 0.009389987, 0.007831596),
tol = 1e7))
## Missing data
x[3,2] < NA
x[4,3] < NA
dt < dStudent(x, df = df, scale = P)
stopifnot(is.na(dt) == rep(c(FALSE, TRUE), each = 2))
## Univariate case
x < matrix(1:10/10, ncol = 1)
dt < dStudent(x, df = df, factor = 1)
dt. < dt(as.vector(x), df = df)
stopifnot(all.equal(dt, dt.))

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