qmvt {mvtnorm} R Documentation

## Quantiles of the Multivariate t Distribution

### Description

Computes the equicoordinate quantile function of the multivariate t distribution for arbitrary correlation matrices based on an inversion of the algorithms by Genz and Bretz.

### Usage

```qmvt(p, interval = c(-10, 10), tail = c("lower.tail", "upper.tail", "both.tails"),
df = 1, delta = 0, corr = NULL, sigma = NULL, maxpts = 25000,
abseps = 0.001, releps = 0, ...)
```

### Arguments

 `p` probability. `interval` 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. `delta` the vector of noncentrality parameters of length n. `df` degree of freedom as integer. `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`. `maxpts` maximum number of function values as integer. `abseps` absolute integration error tolerance as double. `releps` relative integration error tolerance as double. `...` additional paramters to be passed to `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.

### 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`.

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