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From: nuclph nuclph on 17 May 2010 17:29
Hi all,

does any one have an example how to use Matlab capability to generate random normal variables using Sobol sequence? I have stat add in with sobolset but not that clear how to use it to get random normal distribution.


thanks in advance!
From: nuclph nuclph on 17 May 2010 17:55
Hi All,
It seems it is quite easy to do it. See an example below.
Please, let me know if yo have any comments or suggestions.


%test quasi monte carlo
clear all;

nsim = 1000;
nbins = 100;
z_mc = randn(1,nsim);

qmc=sobolset(1,'Skip',1e3);
qmc=net(qmc,nsim);
z_qmc=norminv(qmc,0,1);

subplot(2,1,1);
hist(z_mc,nbins);
title('MC');

subplot(2,1,2);
hist(z_qmc,nbins);
title('Sobol QMC');



"nuclph nuclph" <bskorodo(a)gmail.com> wrote in message <hsscf2$r8g$1(a)fred.mathworks.com>...
> Hi all,
>
> does any one have an example how to use Matlab capability to generate random normal variables using Sobol sequence? I have stat add in with sobolset but not that clear how to use it to get random normal distribution.
>
>
> thanks in advance!
From: Fabian León on 11 Jun 2010 09:47
Hi, I've extended and commented your example. Thanks

% Modified example by Fabian León
% Date: 11 Juny, 2010

clear all;

nsim = 1000; % Vector size.
nbins = 100; % Number of bins used to calculate the histogram.
z_mc = randn(1,nsim); % Returns an 1-by-nsim matrix (size vector = nsim).

s_qmc=sobolset(1,'Skip',nsim); % Set 1-dimensional (vector), and the number
% of initial points to omit (Skip = nsim)
% In this function the diferent sequences
% are set to avoid correlations between each
% vector.
s_qmc=net(s_qmc,nsim); % Get the first nsim points.
z_qmc=norminv(s_qmc,0,1); % Returns the inverse cumulative distribution
% function (cdf) for the normal distribution with
% mean MU(=0) and standard deviation SIGMA (=1),
% evaluated at the values in s_qmc.

h_qmc=haltonset(1,'Skip',nsim-100); % Is the same procedure as in sobol
% case but with halton and another Skip
% value.
h_qmc=net(h_qmc,nsim);
zz_qmc=norminv(h_qmc,0,1);


subplot(3,1,1);
hist(z_mc,nbins);
title('MC');

subplot(3,1,2);
hist(z_qmc,nbins);
title('Sobol QMC');

subplot(3,1,3);
hist(zz_qmc,nbins);
title('Halton QMC');
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