optional, a vector containing the end-points of the
interval to be searched. Does not need to contain the true quantile,
just used as starting values by the root-finder. If equal to NULL
a guess is used.
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 or df = Inf.
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 in the univariate
case (so corr = 1) is used for corr.
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)).
ptol, maxiter, trace
Parameters passed to the stochastic root-finding
algorithm. Iteration stops when the 95% confidence interval
for the predicted quantile is inside [p-ptol, p+ptol]. maxiter is the
maximum number of iterations for the root finding algorithm. trace
prints the iterations of the root finder.
...
additional parameters to be passed to
GenzBretz.
Details
Only equicoordinate quantiles are computed, i.e., the quantiles in each
dimension coincide. The result is seed dependend.
Value
A list with two components: quantile and f.quantile
give the location of the quantile and the difference between the distribution
function evaluated at the quantile and p.