# Dirichlet: Dirichlet distribution In mixAK: Multivariate Normal Mixture Models and Mixtures of Generalized Linear Mixed Models Including Model Based Clustering

## Description

Random number generation for the Dirichlet distribution D(alpha[1],...,alpha[K]).

## Usage

 `1` ```rDirichlet(n, alpha=c(1, 1)) ```

## Arguments

 `n` number of observations to be sampled. `alpha` parameters of the Dirichlet distribution (‘prior sample sizes’).

Some objects.

## Value for rDirichlet

A matrix with sampled values.

## Author(s)

Arnošt Komárek arnost.komarek[AT]mff.cuni.cz

## References

Devroye, L. (1986). Non-Uniform Random Variate Generation. New York: Springer-Verlag, Chap. XI.

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004). Bayesian Data Analysis. Second Edition. Boca Raton: Chapman and Hall/CRC, pp. 576, 582.

`rbeta`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```set.seed(1977) alpha <- c(1, 2, 3) Mean <- alpha/sum(alpha) Var <- -(alpha %*% t(alpha)) diag(Var) <- diag(Var) + alpha*sum(alpha) Var <- Var/(sum(alpha)^2*(1+sum(alpha))) x <- rDirichlet(1000, alpha=alpha) x[1:5,] apply(x, 1, sum)[1:5] ### should be all ones rbind(Mean, apply(x, 2, mean)) var(x) print(Var) ```