RTMBdist (version 0.1.0)

mvt: 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)

Value

dmvt gives the density, rmvt generates random deviates.

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.

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)