qmvt {mvtnorm} | R Documentation |

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.

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, ...)

`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` . |

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.

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`

.

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

[Package *mvtnorm* version 0.7-1 Index]