qmvnorm {mvtnorm}R Documentation

Quantiles of the Multivariate Normal Distribution

Description

Computes the equicoordinate quantile function of the multivariate normal distribution for arbitrary correlation matrices based on inversion of pmvnorm.

Usage

qmvnorm(p, interval = NULL, tail = c("lower.tail", 
        "upper.tail", "both.tails"), mean = 0, corr = NULL, 
        sigma = NULL, algorithm = GenzBretz(), ...)

Arguments

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.

mean

the mean vector of length n.

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, Miwa or TVPACK specifying both the algorithm to be used as well as the associated hyper parameters.

...

additional parameters to be passed to GenzBretz.

Details

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.

Value

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.

See Also

pmvnorm, qmvt

Examples

qmvnorm(0.95, sigma = diag(2), tail = "both")

[Package mvtnorm version 0.9-9994 Index]