Simulation
To simulated a Dirichlet sample quickly we use the method on the Wikipedia page for the Dirichlet distribution.
rdirichlet <- function(N=1,K=c(1,1)) {
# Simulations from the Dirichlet Distribution, according to the method of Wikipedia
lk <- length(K)
sim <- matrix(0,N,lk)
gams <- matrix(0,N,lk)
for (i in 1:lk) {
gams[,i] <- matrix(rgamma(N,K[i]),N,1)
}
gamtotal <- matrix(rowSums(gams),N,lk)
sim <- gams/gamtotal
return(sim)
}
Frequentist Parameter estimation
The simplest method of parameter estimation is the method of moments: