qmvnorm {mvtnorm} | R Documentation |

## Quantiles of the Multvariate Normal Distribution

### Description

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

### Usage

qmvnorm(p, interval = c(-10, 10), tail = c("lower.tail", "upper.tail", "both.tails"),
mean = 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*. |

`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` . |

`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`

.

### See Also

`pmvnorm`

, `qmvt`

### Examples

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

[Package

*mvtnorm* version 0.7-1

Index]