rmvt.mixt, dmvt.mixt: Multivariate t mixture distribution

Description

Random generation and density values from multivariate t mixture distribution.

Usage

rmvt.mixt(n=100, mus=c(0,0), Sigmas=diag(2), dfs=7, props=1)
dmvt.mixt(x, mus, Sigmas, dfs, props)

Arguments

Value

Multivariate t mixture random vectors and density values.

Details

rmvt.mixt and dmvt.mixt are based on the rmvt and dmvt functions from the mvtnorm library.

The formula for a d-variate t density with location vector $\bold{\mu}$, dispersion matrix $\bold{\Sigma}$ and df degrees of freedom is $$k\left[ 1 + \frac{1}{df} (\bold{x} - \bold{\mu})^T \bold{\Sigma}^{-1}(\bold{x} - \bold{\mu}) \right]^{-(d+df)/2}$$ where $$k =\frac{\Gamma((df+d)/2)}{(df\pi)^{d/2} \Gamma(df/2) |\bold{\Sigma}^{1/2}|}.$$

Examples

Run this code

mus <- rbind(c(-3/2,0), c(3/2,0))
Sigmas <- rbind(diag(c(1/16, 1)), rbind(c(1/16, 1/18), c(1/18, 1/16)))
props <- c(2/3, 1/3)
dfs <- c(7,3)
x <- rmvt.mixt(1000, mus, Sigmas, dfs, props)
dens <- dmvt.mixt(x, mus, Sigmas, dfs, props)