How to generate numbers from probability mass function?

Question

Clarisha Nijman 2018-10-9

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回答： PARTHEEBAN R 2021-5-22

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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Answer 1

Torsten 2018-10-9

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编辑：Torsten 2018-10-9

在 MATLAB Online 中打开

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;

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Torsten 2018-10-10

For an explanation, see

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

Clarisha Nijman 2018-10-19

tnx u!

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Answer 2

Bruno Luong 2018-10-9

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在 MATLAB Online 中打开

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

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Clarisha Nijman 2018-10-19

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 3

Jeff Miller 2018-10-20

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image.png

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

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Jeff Miller 2018-10-20

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 2018-10-20

Ok, tnx Jeff, I'll check it!

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Answer 4

PARTHEEBAN R 2021-5-22

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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 ) .