The Dirichlet Distribution

Description

Density function and random number generation for the Dirichlet distribution

Usage

1
rdirichlet(n, alpha)

Arguments

n

number of random observations to draw

alpha

the Dirichlet distribution's parameters. Can be a vector (one set of parameters for all observations) or a matrix (a different set of parameters for each observation), see “Details”

Details

The Dirichlet distribution is a multidimensional generalization of the Beta distribution where each dimension is governed by an alpha-parameter. Formally this is

D(α)=[Γ(∑α)/∏Γ(α)]∏ y^(α-1)

Usually, alpha is a vector thus the same parameters will be used for all observations. If alpha is a matrix, a complete set of alpha-parameters must be supplied for each observation.

Value

returns a matrix with random numbers according to the supplied alpha vector or matrix.

Author(s)

Chong Wu

Examples

1
2
X1 <- rdirichlet(100, c(5, 5, 10))
X1