Dataplot Vol 2 Vol 1

# MULTIVARIATE UNIFORM RANDOM NUMBERS

Name:
MULTIVARIATE UNIFORM RANDOM NUMBER
Type:
Let Subcommand
Purpose:
Generate random numbers from correlated uniform distributions.
Description:
For univariate distributions, Dataplot generates random numbers using the common syntax

LET <shape-parameter> = <value>
LET Y = <dist> RANDOM NUMBERS FOR I = 1 1 N
LET Y = LOC + SCALE*Y

Multivariate distributions, however, generally require matrix operations. For this reason, random numbers for multivariate distributions each have their own unique syntax. Although you can generate P columns of uniform random numbers, this does take into account any correlation between the variables (i.e., they are independent).

To generate correlated uniform random numbers, Dataplot generates correlated multivariate random numbers and then takes the normal cumulative distribution function of these numbers. This algorithm is from Gentle (2003) "Random Number Generation and Monte Carlo Methods".

For details on how to generate uncorrelated multivariate uniform random numbers, enter HELP INDEPENDENT UNIFORM RANDOM NUMBERS.

Syntax:
LET <mat> = MULTIVARIATE UNIFORM RANDOM NUMBERS <sigma> <n>
where <sigma> is a variance-covariance matrix from a multivariate normal distribution;
<n> is a number or parameter specifying the desired number of rows;
and    <mat> is a matrix where the resulting multivariate independent uniform random numbers are stored.

Dataplot determines the number of columns to generate from the number of rows in the matrix.

Examples:
LET M = MULTIVARIATE UNIFORM RANDOM NUMBERS SIGMA N
Note:
Dataplot supports a number of different uniform random number generators. For details, enter

HELP SET RANDOM NUMBER GENERATOR
Default:
None
Synonyms:
CORRELATED UNIFORM RANDOM NUMBERS
Related Commands:
 INDEPENDENT UNIFORM RANDOM NUMBERS = Generate uncorrelated uniform random numbers. RANDOM NUMBERS = Generate random numbers for 60+ univariate distributions. SET RANDOM NUMBER GENERATOR = Specify which univariate generator to use. MULTIVARIATE NORMAL RANDOM NUMBERS = Generate multivariate normal random numbers. MULTIVARIATE T RANDOM NUMBERS = Generate multivariate t random numbers. WISHART RANDOM NUMBERS = Generate random numbers for a Wishart distribution. DIRICHLET RANDOM NUMBERS = Generate random numbers for a Dirichlet distribution.
Reference:
"Random Number Generation and Monte Carlo Methods", Second Edition, James Gentle, Springer-Verlang, 2003, p. 207.
Applications:
Simulation, Bayesian Analysis
Implementation Date:
2003/10
Program:
```
dimension 100 columns
.
1.0   0.5
0.5   1.0
END OF DATA
LET N = 1000
.
CHARACTER .
CHARACTER JUSTIFICATION LEBO
LINE BLANK
.
LET M = MULTIVARIATE UNIFORM RANDOM NUMBERS SIGMA N
.
PLOT M1 VS M2
```

Date created: 2/3/2004
Last updated: 2/3/2004