Normally distributed points within a square in matlab

Question

How can I create N normally distributed points within a N x N square with the mean at the centre (More points concentrated at the centre). I would appreciate an approach in which the coordinates of each points could be stored in a struct. I have tried the code below

 for i=1:200
 S(i).x=randn*200;
 S(i).y=randn*200;
 plot(S(i).x,S(i).y,'.');
 axis([0 200 0 200]); 
 end

However, I observed I got negative values. Using a centre [mean] of (100,100) in a square, I want to store normally distributed points between 0-200 for a 200x200 square. Thanks

Your example generates samples from an uncorrelated normal distribution on the plane. You can use the multi-variable normal distribution function mvnrnd to properly specify both the mean and variance of your distribution. — anon
– anon, Commented Jul 15, 2016 at 13:10

anon · Accepted Answer · 2016-07-15 14:06:08Z

1

The following would require the Statistics Toolbox in MATLAB. You can create a truncated normal distribution, which by definition would only generate normally distributed random numbers within the range [0, N].

% Create a normal distribution
N = 200;
pd = makedist('Normal', 'mu', N/2, 'sigma', 60)

% Truncate the normal distribution to [0,N]
t = truncate(pd, 0, N)

% Samples from normal distribution
x = pd.random(N,1);
y = pd.random(N,1);
subplot(211)
plot(x,y,'bx')
title('Normal Distribution')

% Samples from truncated distribution
x = t.random(N,1);
y = t.random(N,1);
subplot(212)
plot(x,y,'ro')
title('Truncated Normal Distribution')

This would result in something like the following:

answered Jul 15, 2016 at 14:06

anon

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Comments

Shai · Accepted Answer · 2016-07-14 18:41:58Z

0

you should use rand to generate uniformly distributed points.
randn is used for normally distributed points and this is why you get negative values

to center the normally distributed points around 100 you need to add the mean to the result:

S(i).x = randn*200 + 100;

edited Jul 14, 2016 at 18:41

answered Jul 14, 2016 at 18:34

Shai

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3 Comments

Abdulhameed Over a year ago

Thanks! I actually meant normally distributed points. I just made corrections to the question.

Shai Over a year ago

@Abdulhameed unlike uniform distribution, normal distribution is not bounded and you can have values larger than 200and smaller than zero

Abdulhameed Over a year ago

Thanks Shai! Without a bound, the points will not fall into the 200 x 200 dimension. I really appreciate your contribution.

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