MATLAB Answers

## How to generate numbers from probability mass function?

Asked by Clarisha Nijman

### Clarisha Nijman (view profile)

on 9 Oct 2018
Latest activity Commented on by Clarisha Nijman

### Clarisha Nijman (view profile)

on 20 Oct 2018
Accepted Answer by Torsten

### Torsten (view profile)

Hallo,
Given a probability mass function defined as P(X=3)=0.2, P(X=7)=0.3 and P(X=10)=0.5, I want to generate randomly 30 numbers (values for X) with this probability mass function as base. But I really have no idea how and where to start.
Can somebody help me?
Thank you in advance

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## 3 Answers

Answer by Torsten

### Torsten (view profile)

on 9 Oct 2018
Edited by Torsten

### Torsten (view profile)

on 9 Oct 2018
Accepted Answer

n = 30;
X = zeros(n,1);
x = rand(n,1);
X(x <= 0.5) = 10;
X(x > 0.5 & x <= 0.8) = 7;
X(x > 0.8) = 3;

Clarisha Nijman

### Clarisha Nijman (view profile)

on 9 Oct 2018
Thanks a lot Torsten,
I do not fully understand the code, But it works!!!!
kind regards
Torsten

### Torsten (view profile)

on 10 Oct 2018
For an explanation, see
https://stats.stackexchange.com/questions/26858/how-to-generate-numbers-based-on-an-arbitrary-discrete-distribution
Clarisha Nijman

### Clarisha Nijman (view profile)

on 19 Oct 2018
tnx u!

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Answer by Bruno Luong

### Bruno Luong (view profile)

on 9 Oct 2018

A more generic method:
p = [0.2 0.3 0.5];
v = [3 7 10];
n = 10000;
c = cumsum([0,p(:).']);
c = c/c(end); % make sur the cumulative is 1
[~,i] = histc(rand(1,n),c);
r = v(i); % map to v values

Clarisha Nijman

### Clarisha Nijman (view profile)

on 19 Oct 2018
This answer works for me the best. I need this to do random column sampling (sampling some columns of a very big matrix A)

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Answer by Jeff Miller

### Jeff Miller (view profile)

on 20 Oct 2018

With Cupid you could write:

```v = [3 7 10];       % the values
p = [0.2 0.3 0.5];  % their probabilities
rv = List(v,p);     % a random variable with those values & probabilities
n = 10000;
randoms = rv.Random(n,1);  % generate n random values of the random variable
```

Clarisha Nijman

### Clarisha Nijman (view profile)

on 20 Oct 2018
Hi Jeff, your suggestion give me three problems
1.Shouldn't the 3rd line be: rv=[v;p]? It gives an error.
2.The last line does not work and I have no idea how to replace it.
3.Where does the code take the cumulative distribution into account? Should simulation not be based on flipping a coin, choosing at random a prob and then determine based on the cumulative distribution what should be drawn?
Please let me know, thank you in advance
kind regards,
Jeff Miller

### Jeff Miller (view profile)

on 20 Oct 2018
Did you download the Cupid files (see the link in my answer)? These define the List class (which handles the cumulative distribution behind the scene). Do the other Cupid demos run correctly?
Well, Cupid may be overkill for your problem, but it does have a lot of flexibility.
Clarisha Nijman

### Clarisha Nijman (view profile)

on 20 Oct 2018
Ok, tnx Jeff, I'll check it!

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