R: Quantiles of the Multivariate Normal Distribution

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(),
            ptol = 0.001, maxiter = 500, trace = FALSE, ...)

### Arguments

`p` | probability.
`interval` | 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.
`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.
`ptol, maxiter, trace` | 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`.

### Details

Only equicoordinate quantiles are computed, i.e., the quantiles in each dimension coincide. The result is seed dependend.

### Value

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`.

### See Also

`pmvnorm`, `qmvt`

### Examples

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

[Package mvtnorm version 1.0-6 Index]