qmvt: Quantiles of the Multivariate t Distribution

Description

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

Usage

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"), ...)

Arguments

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 $P[X \le x] = p$, upper.tail gives $x$ with $P[X > x] = p$ and both.ta

delta

the vector of noncentrality parameters of length n, for type = "shifted" delta specifies the mode.

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 sigm

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

...

additional parameters to be passed to GenzBretz.

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.

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.

Examples

Run this code

qmvt(0.95, df = 16, tail = "both")