Generate a random number with max, min and mean (average) in Matlab

Question

I need to generate random numbers with following properties.

• Min must be 1
• Max must be 9
• Average (mean) is 6.00 (or something else)
• Random number must be Integer (positive) only

I have tried several syntaxes but nothing works, for example

r=1+8.*rand(100,1);

This gives me a random number between 1-9 but it's not an integer (for example 5.607 or 4.391) and each time I calculate the mean it varies.

• Jonas: What shape do you want for your distribution?
• yuk: For any RNG don't expect the mean will always be exactly as you specify, it will vary from run to run. With larger N it can be closer though.
• Chanon: type of distribution is not importance, just want mean is the same for each set of random numbers.

Answer 1

You may be able to define a function that satisfies your requirements based on Matlab's randi function. But be careful, it is easy to define functions of random number generators which do not produce random numbers.

Another approach might suit -- create a probability distribution to meet your requirements. In this case you need a vector of 9 floating-point numbers which sum to 1 and which, individually, express the probability of the i-th integer occurring. For example, a distribution might be described by the following vector:

[0.1 0.1 0.1 0.1 0.2 0.1 0.1 0.1 0.1]

These split the interval [0,1] into 9 parts. Then, take your favourite rng which generates floating-point numbers in the range [0,1) and generate a number, suppose it is 0.45. Read along the interval from 0 to 1 and you find that this is in the 5-th interval, so return the integer 5.

Obviously, I've been too lazy to give you a vector which gives 6 as the mean of the distribution, but that shouldn't be too hard for you to figure out.

Answer 2

Here is an algorithm with a loop to reach a required mean xmean (with required precision xeps) by regenerating a random number from one half of a vector to another according to mean at current iteration. With my tests it reached the mean pretty quick.

n = 100;
xmean = 6;
xmin = 1;
xmax = 9;
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([xmean xmax]);
 elseif xmean < mean(x)
 x(find(x > xmean,1)) = randi([xmin xmean]);
 end
end

x is the output you need.

• Chanon: this syntax give me --- ??? Undefined function or method 'randi' for input arguments of type 'double'.---- T-T help me pls.
• yuk: Function randi (to generate random integers) appeared first in MATLAB version 2008b. Probably yours is older. See this SO answer.
• Chanon: the algorithm that you gave to me just work fine on MATLAB2010b, thanks to you alot ^^ but sometime mean is not integer number such as 6.65 or 4.77 then this algorithm rejected to generate number for me T-T how can I use mean that is not integer ?
• yuk: You've never said the mean has to be integer what you need it for. Please explain. And what is T-T?
• Chanon: I'm so sorry about didn't told you clearly ^^" and want to say thanks to you a lot again, yuk. Your algorithm just save my life for a while. I have to say I'm new to MATLAB or statistic like this, never do this before in my life but still try to learn. So, it is possible to set mean in to not-integer value ? This set of random numbers I'll use to prove something that hard to explain with my broken english like this ^^" Just in case, sometimes mean is not integer value and this algorithm failed to generate ^^ so, it is possible ?

Answer 3

You can use randi to get random integers

Answer 4

You could use floor to truncate your random numbers to integer values only:

r = 1 + floor(9 * rand(100,1));

Obtaining a specified mean is a little trickier; it depends what kind of distribution you're after.

• Chanon: any kind of distribution is okay, just the same mean every generate.

Answer 5

If the distribution is not important and all you're interested in is the mean, then there's a particularly simple function that does that:

function x=myrand
 x=6;
end

• SecretAgentMan: This won't generate a random number at all...it generates 6 with probability 1.

Answer 6

Before you can design your random number generator you need to specify the distribution it should draw from. You've only partially done that: i.e., you specified it draws from integers in [1,9] and that it has a mean that you want to be able to specify. That still leaves an infinity of distributions to chose among. What other properties do you want your distribution to have?

Edit following comment: The mean of any finite sample from a probability distribution - the so-called sample mean - will only approximate the distribution's mean. There is no way around that.

That having been said, the simplest (in the maximum entropy sense) distribution over the integers in the domain [1,9] is the exponential distribution: i.e.,

p = @(n,x)(exp(-x*n)./sum(exp(-x*(1:9))));

The parameter x determines the distribution mean. The corresponding cumulative distribution is

c = cumsum(p(1:9,x));

To draw from the distribution p you can draw a random number from [0,1] and find what sub-interval of c it falls in: i.e.,

samp = arrayfun(@(y)find(y<c,1),rand(n,m));

will return an [n,m] array of integers drawn from p.

• Chanon: any type of distribution is okay, type of distribution is not importance, just want mean is the same for each set of random numbers. thanks.