qmvt  R Documentation 
Computes the equicoordinate quantile function of the multivariate t
distribution for arbitrary correlation matrices
based on inversion of pmvt
, using a stochastic root
finding algorithm described in Bornkamp (2018).
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"), ptol = 0.001, maxiter = 500,
trace = FALSE, seed = NULL, ...)
p 
probability. 
interval 
optional, a vector containing the endpoints of the interval to be searched. Does not need to contain the true quantile, just used as starting values by the rootfinder. If equal to NULL a guess is used. 
tail 
specifies which quantiles should be computed.

delta 
the vector of noncentrality parameters of length n, for

df 
degree of freedom as integer. Normal quantiles are computed
for 
corr 
the correlation matrix of dimension n. 
sigma 
the covariance matrix of dimension n. Either 
algorithm 
an object of class 
type 
type of the noncentral multivariate t distribution
to be computed. The choice 
ptol , maxiter , trace 
Parameters passed to the stochastic rootfinding
algorithm. Iteration stops when the 95% confidence interval
for the predicted quantile is inside [pptol, p+ptol]. 
seed 
an object specifying if and how the random number generator
should be initialized, see 
... 
additional parameters to be passed to

Only equicoordinate quantiles are computed, i.e., the quantiles in each dimension coincide. The result is seed dependend.
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
.
Bornkamp, B. (2018). Calculating quantiles of noisy distribution functions using local linear regressions. Computational Statistics, 33, 487–501.
pmvnorm
, qmvnorm
## basic evaluation
qmvt(0.95, df = 16, tail = "both")
## check behavior for df=0 and df=Inf
Sigma < diag(2)
set.seed(29)
q0 < qmvt(0.95, sigma = Sigma, df = 0, tail = "both")$quantile
set.seed(29)
q8 < qmvt(0.95, sigma = Sigma, df = Inf, tail = "both")$quantile
set.seed(29)
qn < qmvnorm(0.95, sigma = Sigma, tail = "both")$quantile
stopifnot(identical(q0, q8),
isTRUE(all.equal(q0, qn, tol = (.Machine$double.eps)^(1/3))))
## if neither sigma nor corr are provided, corr = 1 is used internally
df < 0
set.seed(29)
qt95 < qmvt(0.95, df = df, tail = "both")$quantile
set.seed(29)
qt95.c < qmvt(0.95, df = df, corr = 1, tail = "both")$quantile
set.seed(29)
qt95.s < qmvt(0.95, df = df, sigma = 1, tail = "both")$quantile
stopifnot(identical(qt95, qt95.c),
identical(qt95, qt95.s))
df < 4
set.seed(29)
qt95 < qmvt(0.95, df = df, tail = "both")$quantile
set.seed(29)
qt95.c < qmvt(0.95, df = df, corr = 1, tail = "both")$quantile
set.seed(29)
qt95.s < qmvt(0.95, df = df, sigma = 1, tail = "both")$quantile
stopifnot(identical(qt95, qt95.c),
identical(qt95, qt95.s))
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