Choosing from a range of numbers with normal distribution

Question

I need to choose one pixel from a range of, for example, 0 to 1920 pixels with the normal distribution, but I have no idea how to do this in MatLab. I know that I can use normrnd() to retrieve a random value given mu and sigma, but how do I apply this to my situation?

mu might be at 500 pixels and sigma 100 pixels, for example.

My current approach is this

function xpos = apply_normal_distribution(mu, sigma, min_xpos=1, max_xpos=1920)
    % Applies normal distribution with median mu and standard deviation sigma
    % xpos will always be: min <= xpos <= max
    xpos = ceil(normrnd(mu, sigma));
    if xpos > max_xpos
        xpos = max_xpos;
    elseif xpos < min_xpos
        xpos = min_xpos;
    endif
end

So I'm just using normrnd and cutting off if the value is higher or lower than my bounds. Don't know how good this is, but it works.

Answer 1

The moment you bound a normal distribution (or filter its results in any other way) it is not a normal distribution anymore. However, there exists a truncated normal distribution which is the closest thing to what you are looking for. It has it's own set of properties which are similar to a normal distribution if the bounds are far away from the mean and you have a low variance. With Matlab you can make that with:

mu = 500;
sigma = 100;
%truncate at 0 and 1920
pd = truncate(makedist('Normal',mu,sigma),0,1920);
% take some (10) samples
samples = random(pd,10,1);

Building it from scratch for Octave:

Your self-made proposal has the problem that if a realisation is outside the bound, you set the value to the bound value. Therefore the bound value will be overly proportional chosen. A less dirty way is instead to just draw a fresh value. I don't have a working Octave, but something like this should do it:

function xpos = apply_normal_distribution(mu, sigma, min_xpos=1, max_xpos=1920)
    % new realisations are drawn as long as they are outside the bounds.
    while xpos<min_xpos | xpos>max_xpos 
            xpos = ceil(normrnd(mu, sigma));
    end
end

Just as a warning: If it is unlikely that a realisation will be within the bounds then this may run for a very long time...