How can I generate a vector of random numbers using the normal distribution?

[Krzysztof W]

Dear all,

could you tell me how can I generate a vector of random numbers using the normal distribution in AMPL with mean and variance listed below?

param mean :=

1   45

2   35

3   40;

param variance :

    1       2       3 :=

1   1      -2      -1

2  -2      36      -8

3  -1      -8       9;

Kind regards,

Krzystof

[Robert Fourer]

AMPL and its extended function library (http://ampl.com/resources/extended-function-library/) only provide samples from univariate random distributions. If you know or can compute an AA^T factorization of your n x n covariance matrix, then you can compute a multivariate normal sample from n univariate samples -- according to http://en.wikipedia.org/wiki/Multivariate_normal_distribution#Drawing_values_from_the_distribution. Alternatively you may use a math or stat system (MATLAB, R, ...) to compute multivariate normal samples and then read them as data into AMPL.

Bob Fourer
am...@googlegroups.com

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