How to generate numbers from probability mass function?

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

Answer 1

[Torsten]

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]

Thanks a lot Torsten,

I do not fully understand the code, But it works!!!!

kind regards

[Torsten]

For an explanation, see

https://stats.stackexchange.com/questions/26858/how-to-generate-numbers-based-on-an-arbitrary-discrete-distribution

[Clarisha Nijman]

tnx u!

Answer 2

[Bruno Luong]

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]

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

Answer 3

[Jeff Miller]

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]

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]

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]

Ok, tnx Jeff, I'll check it!

Answer 4

[PARTHEEBAN R]

A random variable X has cdf F(x) = { 0 , if x < − 1 a(1 + x ) , if − 1 < < 1 1 , if x ≥ 1 . Find (1) the value of a, (2) P(X > 1/4 ) and P ( − 0 . 5 ≤ X ≤ 0 ) .