R: The Dirichlet Random Vector Generating Function

rdirichlet {rBeta2009}

R Documentation

The Dirichlet Random Vector Generating Function

Description

The function to generate random vectors from the Dirichlet distribution.

Usage

 rdirichlet(n, shape)

Arguments

`n`	Number of Dirichlet random vectors to generate. If `length(n) > 1`, the length is taken to be the number required.
`shape`	Vector with `length(shape) >= 2` containing positive shape parameters of the Dirichlet distribution. If `length(shape) = 2`, it reduces to the beta generating function.

Details

The Dirichlet distribution is the multidimensional generalization of the beta distribution.

A k-variate Dirichlet random vector (x_1,\ldots,x_k) has the joint probability density function

\frac{\Gamma(\alpha_1+\dots+\alpha_{k+1})}{\Gamma(\alpha_1)\dots\Gamma(\alpha_{k+1})} x_1^{\alpha_1-1}\dots x_k^{\alpha_k-1}\left(1-\sum_{i=1}^k x_i\right)^{\alpha_{k+1}-1},

where x_i \ge 0 for all i = 1, \ldots, k, \sum_{i=1}^k x_i \leq 1, and \alpha_1, \ldots, \alpha_{k+1} are positive shape parameters.

rdirichlet generates the Dirichlet random vector by utilizing the transformation method based on beta variates and three guidelines introduced by Hung et al. (2011). The three guidelines include: how to choose the fastest beta generation algorithm, how to best re-order the shape parameters, and how to reduce the amount of arithmetic operations.

Value

rdirichlet() returns a matrix with n rows, each containing a single Dirichlet random vector.

Author(s)

Ching-Wei Cheng <aks43725@gmail.com>,
Ying-Chao Hung <hungy@nccu.edu.tw>,
Narayanaswamy Balakrishnan <bala@univmail.cis.mcmaster.ca>

Source

rdirichlet uses a C translation of

Y. C. Hung and N. Balakrishnan and C. W. Cheng (2011), Evaluation of algorithms for generating Dirichlet random vectors, Journal of Statistical Computation and Simulation, 81, 445–459.

References