qmvt {mvtnorm} | R Documentation |
Computes the equicoordinate quantile function of the multivariate t distribution for arbitrary correlation matrices based on inversion of qmvt.
qmvt(p, interval = NULL, tail = c("lower.tail", "upper.tail", "both.tails"), df = 1, delta = 0, corr = NULL, sigma = NULL, algorithm = GenzBretz(), type = c("Kshirsagar", "shifted"), ...)
p |
probability. |
interval |
optional, a vector containing the end-points of the interval to be
searched by uniroot . |
tail |
specifies which quantiles should be computed.
lower.tail gives the quantile x for which
P[X ≤ x] = p, upper.tail gives x with
P[X > x] = p and
both.tails leads to x
with P[-x ≤ X ≤ x] = p. |
delta |
the vector of noncentrality parameters of length n, for
type = "shifted" delta specifies the mode. |
df |
degree of freedom as integer. Normal quantiles are computed for df = 0 . |
corr |
the correlation matrix of dimension n. |
sigma |
the covariance matrix of dimension n. Either corr or
sigma can be specified. If sigma is given, the
problem is standardized. If neither corr nor
sigma is given, the identity matrix is used
for sigma . |
algorithm |
an object of class GenzBretz or
TVPACK defining the
hyper parameters of this algorithm. |
type |
type of the noncentral multivariate t distribution
to be computed. type = "Kshirsagar" corresponds
to formula (1.4) in Genz and Bretz (2009) (see also
Chapter 5.1 in Kotz and Nadarajah (2004)) and
type = "shifted" corresponds to the formula before
formula (1.4) in Genz and Bretz (2009)
(see also formula (1.1) in Kotz and Nadarajah (2004)). |
... |
additional parameters to be passed to
GenzBretz . |
Only equicoordinate quantiles are computed, i.e., the quantiles in each
dimension coincide. Currently, the distribution function is inverted by
using the
uniroot
function which may result in limited accuracy of the
quantiles.
A list with four components: quantile
and f.quantile
give the location of the quantile and the value of the function
evaluated at that point. iter
and estim.prec
give the number
of iterations used and an approximate estimated precision from
uniroot
.
qmvt(0.95, df = 16, tail = "both")