mvtnorm-package: Multivariate Normal and t Distributions In mvtnorm: Multivariate Normal and t Distributions

 mvtnorm-package R Documentation

Multivariate Normal and t Distributions

Description

Computes multivariate normal and t probabilities, quantiles, random deviates, and densities. Log-likelihoods for multivariate Gaussian models and Gaussian copulae parameterised by Cholesky factors of covariance or precision matrices are implemented for interval-censored and exact data, or a mix thereof. Score functions for these log-likelihoods are available. A class representing multiple lower triangular matrices and corresponding methods are part of this package.

Details

Package mvtnorm provides functionality for dealing with multivariate normal and t-distributions. The package interfaces FORTRAN and `C` code for evaluating multivariate normal probabilities written by Alan Genz and Tetsuhisa Miwa. Functions `pmvnorm`, `pmvt`, `qmvnorm`, and `qmvt` return normal and t probabilities or corresponding quantiles computed by these original implementations. Users interested in the computation of such probabilities or quantiles, for example for multiple testing purposes, should use this functionality.

When the multivariate normal log-likelihood function, defined by the log-probability in the discrete or interval-censored case or by the log-density for exact real observations, or a mix thereof, shall be computed, functions `lpmvnorm`, `ldmvnorm`, and `ldpmvnorm` are better suited. They rely on an independent implementation of Genz' algorithm (for log-probabilities), can be customised (different quasi-Monte Carlo schemes), and are a bit faster. Most importantly, the corresponding score functions are available through functions `slpmvnorm`, `sldmvnorm`, or `sldpmvnorm`, which help to speed-up parameter estimation considerably. Users interested in this functionality should consult the `lmvnorm_src` package vignette.

`vignette("lmvnorm_src", package = "mvtnorm")`