extraDistr (version 1.10.0)

Dirichlet: Dirichlet distribution

Description

Density function, cumulative distribution function and random generation for the Dirichlet distribution.

Usage

ddirichlet(x, alpha, log = FALSE)
rdirichlet(n, alpha)

Arguments

x

\(k\)-column matrix of quantiles.

alpha

\(k\)-values vector or \(k\)-column matrix; concentration parameter. Must be positive.

log

logical; if TRUE, probabilities p are given as log(p).

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Probability density function $$ f(x) = \frac{\Gamma(\sum_k \alpha_k)}{\prod_k \Gamma(\alpha_k)} \prod_k x_k^{k-1} $$

References

Devroye, L. (1986). Non-Uniform Random Variate Generation. Springer-Verlag.

Examples

# Generating 10 random draws from Dirichlet distribution
# parametrized using a vector

rdirichlet(10, c(1, 1, 1, 1))

# or parametrized using a matrix where each row
# is a vector of parameters

alpha <- matrix(c(1, 1, 1, 1:3, 7:9), ncol = 3, byrow = TRUE)
rdirichlet(10, alpha)