Generate random numbers with specific mean

I want to generate matrix 4*4 of random integer values from 0 to 255, i used randi([0 255],4) but i want to generate it with specific mean for example 200 so i used:

z = randi([0 255],4)

z = z + (200 - mean2(z))

that did fix mean value but it could change min and max value of integers, How can i fix it ??!

[the cyclist]

There are an infinite number of ways to generate random integers that have the following properties:

• max = 255
• min = 0
• mean = 200

For example,

N = 1000000;
p = 200/255;
x = 255 * (rand(N,1) < p);

mean(x) % Will be equal to 200, within sampling error

ans = 200.2543

figure
histogram(x)

This distribution obeys the rules you have told us. And, as I said, there are infinite others. You need more specificity on the distribution.

[Amr Ayman]

you're right, I should have been more specific about what i wanted but I couldn't explain what I needed more than that

Answer 1

[Matt J]

You can use this FEX download

https://www.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum?s_tid=srchtitle

m=4;n=4; targetMean=200;

z = randfixedsum(m*n,1,targetMean*m*n,0,255);

z=reshape(z,m,n);

mean(z(:))

ans =

200.0000

[Amr Ayman]

this is what i needed, Thanks alot

[the cyclist]

I would encourage you to think carefully about whether this function truly does what you need.

Specifically, this function will return values that always sum to 200. This is different from saying you want to draw values from a distribution that will give a mean value of 200.

Draw an analogy with coin-flipping: There is a difference between

• flip 10 coins, and on average get 5 tails
• flip 10 coins, and always get 5 tails

The randfixedsum function is more like doing the latter. Maybe that's what you need, but maybe not.

[the cyclist]

Also, randomfixedsum generates real values, not integer values.

[Amr Ayman]

Thanks for your comment but yes it was what i wanted

As it will generate different matrix each time but with the specific mean i gave it, Yeh it will always get 200 not 200 on avergae but it's okay for me.

And yeah it generates real values not integer so i added floor after reshaping "which will make value of mean slightly change around 200 not to be always 200 :)) "

[the cyclist]

OK.

FYI, there is something known as the beta-binomial distribution that I believe would also have the properties you described (but with integer values inherently). I don't think MATLAB has an implementation of it, but it looks like this File Exchange submission does it.

[Amr Ayman]

Thanks, I will look at it

[Matt J]

There is a difference between

• flip 10 coins, and on average get 5 tails
• flip 10 coins, and always get 5 tails

There can be a difference, but note that the second always implies the first.

And yeah it generates real values not integer so i added floor after reshaping "which will make value of mean slightly change around 200 not to be always 200 :)) "

In fact, if you apply round() instead of floor(), I would expect the statistical average to remain at 200, even if the nonstatistical average mean(z(:)) does not remain perfectly at 200.