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.
Value
dmvt gives the density, rmvt generates random deviates.
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)