dmvt.mixt, rmvt.mixt {ks} | R Documentation |
Random generation and density values from multivariate t mixture distribution.
rmvt.mixt(n=100, mus=c(0,0), Sigmas=diag(2), dfs=7, props=1) dmvt.mixt(x, mus, Sigmas, dfs, props)
n |
number of random variates |
x |
matrix of quantiles |
mus |
(stacked) matrix of location vectors |
Sigmas |
(stacked) matrix of dispersion matrices |
dfs |
vector of degrees of freedom |
props |
vector of mixing proportions |
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 mu, dispersion matrix Sigma and df degrees of freedom is
gamma((df+d)/2) / ((df*pi)^(d/2) * gamma(df/2)* det(Sigma)^(1/2) * (1 + 1/df * (x-mu)^T * Sigma^(-1) (x-mu))^(-(d+df)/2).
Multivariate t mixture random vectors and density values.
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)