Computes the equicoordinate quantile function of the multivariate normal
distribution for arbitrary correlation matrices
based on inversion of pmvnorm, using a stochastic root
finding algorithm described in Bornkamp (2018).
qmvnorm(p, interval = NULL, tail = c("lower.tail",
"upper.tail", "both.tails"), mean = 0, corr = NULL,
sigma = NULL, algorithm = GenzBretz(),
ptol = 0.001, maxiter = 500, trace = FALSE, ...)probability.
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.
specifies which quantiles should be computed.
lower.tail gives the quantile \(x\) for which
\(P[X \le x] = p\), upper.tail gives \(x\) with
\(P[X > x] = p\) and
both.tails leads to \(x\)
with \(P[-x \le X \le x] = p\).
the mean vector of length n.
the correlation matrix of dimension n.
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.
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.
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.
Only equicoordinate quantiles are computed, i.e., the quantiles in each dimension coincide. The result is seed dependend.
Bornkamp, B. (2018). Calculating quantiles of noisy distribution functions using local linear regressions. Computational Statistics, 33, 487--501.
# NOT RUN {
qmvnorm(0.95, sigma = diag(2), tail = "both")
# }
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