generating random numbers from binomial distribution

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Atakan
Atakan 2012-1-23
To generate Bin(4, 3/4), use the following table:
x 0 1 2 3 4
P(X=x) 1/256 3/64 54/256 27/64 81/256
I want to write the MATLAB code to generate 5 random numbers from this distribution. I must use the following algorithm:
Algorithm:
1.Generate u from UNIF(0,1).
2.If P(X <= j-1) <= u <= P(X <= j) then set X=j for j=1,2,3,4
I have written the following code. But I think this code is a general code for generating from Binomial. How can I specialize it to my algorithm?
function X = dene(n,p,N)
X = zeros(1,N); % Generate the uniform random numbers: % N variates of n trials.
U = rand(N,n); % Loop over the rows, finding the number % less than p
for i = 1:N
ind = find(U(i,:) <= p);
X(i) = length(ind);
end
end

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采纳的回答

the cyclist
the cyclist 2012-1-23
OK. I was right about cumsum, but there was another error. For each trial, when you generate the uniform random, you do not need to generate a vector of 5 of those values. You should just generate 1 value, to then compare against the cumulative value of p. I've fixed it up here. I also added a little plot to illustrate the distribution. (Hope I did not just do your homework for you.)
X = zeros(1,N); % Generate the uniform random numbers: % N variates of n trials.
U = rand(N,1); % Loop over the rows, finding the number % less than p
for i = 1:N
ind = find(U(i) <= cumsum(p));
X(i) = length(ind);
end
h = hist(X,unique(X))
count = fliplr(h)/sum(h)
figure
bar(unique(X),count)
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the cyclist
the cyclist 2012-1-24
When you say "generated numbers", I assume you are talking about the output "X". I do not get only 0s and 1s, so I guess we are calling the function differently. Here is what I do. First, the code as I have written above is inside the function dene.m, where the first line of the function is:
function X = dene(n,p,N)
Then, in the base workspace, I define the inputs:
n = 5; % The function does not actually use this input anymore!
N = 10000;
p = [1/256 3/64 54/256 27/64 81/256];
Then, I call dene() with the inputs:
X = dene(n,p,N);
What I get for output is a series of integers, ranging from 1 to 5. The frequency distribution is (approximately) the probability p that you input. (The ordering is reversed relative to p, which I did not quite figure out, I must admit.)
Atakan
Atakan 2012-1-24
I think you are right. If I assign only one value to p the output contains only 1 and 0. Also I wonder about that our code involves the 2. algorithm which is:
If P(X <= j-1) <= u <= P(X <= j) then set X=j for j=1,2,3,4

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更多回答（1 个）

the cyclist
the cyclist 2012-1-23
I have not looked at your algorithm in detail, but here's a guess. Where you have p inside your loop, I think you might want cumsum( p ) instead. Then you are checking to see if your randomly generated value is less that the cumulative probability distribution, which I think is what you want.
  2 个评论
Atakan
Atakan 2012-1-23
Thank you for your suggestion. But still i cannot combine it with the algorithm.
the cyclist
the cyclist 2012-1-23
OK. I'll try to take a closer look. Maybe you could add a little more details about why you think the results are incorrect. How many trials are you running?

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