mvt: Multivariate t distribution

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

Multivariate t distribution

Description

Density and and random generation for the multivariate t distribution

Usage

dmvt(x, mu, Sigma, df, log = FALSE)

rmvt(n, mu, Sigma, df)

Arguments

x	vector or matrix of quantiles
mu	vector or matrix of location parameters (mean if df > 1)
Sigma	positive definite scale matrix (proportional to the covariance matrix if df > 2)
df	degrees of freedom; must be positive
log	logical; if TRUE, densities p are returned as \log(p).
n	number of random values to return.

Details

This implementation of dmvt allows for automatic differentiation with RTMB.

Note: for df \le 1 the mean is undefined, and for df \le 2 the covariance is infinite. For df > 2, the covariance is df/(df-2) * Sigma.

Value

dmvt gives the density, rmvt generates random deviates.

Examples

# single mu
mu <- c(1,2,3)
Sigma <- diag(c(1,1,1))
df <- 5
x <- rmvt(2, mu, Sigma, df)
d <- dmvt(x, mu, Sigma, df)
# vectorised over mu
mu <- rbind(c(1,2,3), c(0, 0.5, 1))
x <- rmvt(2, mu, Sigma, df)
d <- dmvt(x, mu, Sigma, df)

RTMBdist documentation built on April 1, 2026, 5:07 p.m.