Dataplot Vol 2 Vol 1

# DIRICHLET RANDOM NUMBER

Name:
DIRICHLET RANDOM NUMBER
Type:
Let Subcommand
Purpose:
Generate random numbers from a Dirichlet distribution.
Description:
The Dirichlet distribution is a generalization of the beta distribution. To generate a matrix of Dirichlet random numbers with n rows and k columns, k independent vectors of length n containing independent gamma random numbers are generated. The numbers in each column are divided by the sum of that column.

If there are two shape parameters, the Dirichlet distribution reduces to a Beta distribution. In addition, the marginal distribution of each column is also a beta distribution.

Syntax:
LET <mat> = DIRICHLET RANDOM NUMBERS <alpha> <n>
where <alpha> is a variable containing the desired shape (> 0) parameters;
<n> is a number or parameter specifying the desired number of observations;
and where <mat> is a matrix where the resulting Dirichlet random numbers are stored.
Examples:
LET ALPHA = DATA 1 2 3
LET N = 1000
LET M = DIRICHLET RANDOM NUMBERS ALPHA N
Note:
Dataplot uses a Fortran translation of the "gsl_ran_dirichlet" code (written by Gavin Crooks) from the GNU GSL library to generate the Dirichlet random numbers.
Note:
As with univariate random numbers, the multinomial random numbers are built on an underlying uniform random number generator. Dataplot supports a number of different uniform random number generators. For details, enter

HELP SET RANDOM NUMBER GENERATOR
Default:
None
Synonyms:
None
Related Commands:
 RANDOM NUMBERS = Generate random numbers for 90+ univariate distributions. SET RANDOM NUMBER GENERATOR = Specify which univariate generator to use. MULTIVARIATE NORM RAND NUMB = Generate multivariate normal random numbers. MULTIVARIATE T RANDOM NUMBERS = Generate multivariate t random numbers. INDEPENDENT UNIFORM RAND NUMB = Generate random numbers for independent uniform distributions. WISHART RANDOM NUMBERS = Generate random numbers for a Wishart distribution. MULTINOMIAL RANDOM NUMBERS = Generate random numbers for a multinomial distribution.
Reference:
"Statistical Distributions: Third Edition", Evans, Hastings, and Peacock, Wiley, 2000, pp. 62-64.
Applications:
Simulation, Bayesian Analysis
Implementation Date:
2003/5
Program:
```
dimension 100 columns
.
let alpha = data 0.5 1.0 1.5 2.0
let n = 500
.
let d = dirichlet random numbers alpha n
.
title automatic
xlimits 0 1
xtic offset 0.2 0.2
multiplot corner coordinates 0 0 100 100
multiplot 2 2
relative histogram d1
relative histogram d2
relative histogram d3
relative histogram d4
end of multiplot
```

Date created: 7/7/2004
Last updated: 7/7/2004