Generate random numbers with conditions (min, max, mean, and specific values)

Hi! I'm very new at Matlab and I would like some tips to solve the following issue ...

I would like to generate a sequence of 40 random numbers (floats) (min=8, max=20, mean=10). However, 4 of these numbers must be equal to 16. How do you solve this question?

[John D'Errico]

It cannot be done, UNLESS you specify the distribution of the numbers you have not chosen already.

So pick 4 numbers equal to 16. Don't worry about the order, since you can always randomize the set.

What is left, now you have a set of random numbers, but with no distribution specified. Random means nothing, if you do not specify the distribution. Yes, you could compute the mean of the numbers that remain, but that is irrelevant.

[carolina travassos]

Sorry, I completly forgot to mention that. It is from a normal distribution!

[the cyclist]

A normal distribution, by definition, does not have a minimum or maximum possible value. So, the things you say that you want are inconsistent.

Perhaps you can describe why you need these numbers, and we can help figure out your confusion.

[carolina travassos]

Perhaps I explained myself wrong, sorry ... I wanna pick up different sequences of 40 random numbers from a normal distribution. That sequences must have numbers between 8 and 20, a mean=10, and 4 of these numbers must be equal to 16.

These numbers are interstimulus intervals from a psychophysics experiment.

[the cyclist]

I will also try to be clearer. You cannot have both of these things:

• numbers between 8 and 20
• numbers from a normal distribution

These are mathematically contradictory facts. It is like saying you want a number that is both bigger than 3, and smaller than 2. It just cannot be.

You need to figure out how to reconcile these facts. Often, people don't really understand what a normal distribution is, and they might be OK with some other random distribution. Or sometimes they are OK with a truncated normal. But, we cannot figure that out for you.

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/886094-normally-distributed-random-numbers-with-fixed-sum#answer_754514 might help with generating the 4 values that have a fixed sum. Then you generate another 36 values. Then you randperm() the vector of 40 values.

Answer 1

[Dev]

You might be aware that at least 4 numbers are going to be 16, so you have to generate 36 random numbers with mean 28/3. If type of distribution doesn’t matter, You can use the following code to generate such distribution.

n = 36; 
xmean = 28/3; 
xmin = 8; 
xmax = 20; 
xeps = 0.01; 
x = randi([xmin xmax],n,1); 
while abs(xmean - mean(x)) >= xeps 
    if xmean > mean(x) 
        x(find(x < xmean,1)) = randi([ceil(xmean) xmax]); 
    elseif xmean < mean(x) 
        x(find(x > xmean,1)) = randi([xmin floor(xmean)]); 
    end 
end 

Answer 2

[Bruno Luong]

Use this fex

https://fr.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum

r = randperm([16+zeros(4,1); randfixedsum(36,1,40*10-16*4,8,20)]);
p=randperm(40);
r=r(p)

Most of numbers are around 10 since the MEAN pull the numbers arouns that value, so the chance to get big number (20) is tiny.