Conditional Random number generation
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Hello there, For example; If I want to generate 5 random integer numbers with a sum of 20, how can I do that?
" ... example = ceil(10*rand(100, 5)) ... "
Accepted Answer
Roger Stafford
on 4 Mar 2017
function R = randfixedsumint(m,n,S);
% This generates an m by n array R. Each row will sum to S, and
% all elements are all non-negative integers. The probabilities
% of each possible set of row elements are all equal.
% RAS - Mar. 4, 2017
if ceil(m)~=m|ceil(n)~=n|ceil(S)~=S|m<1|n<1|S<0
error('Improper arguments')
else
P = ones(S+1,n);
for in = n-1:-1:1
P(:,in) = cumsum(P(:,in+1));
end
R = zeros(m,n);
for im = 1:m
s = S;
for in = 1:n
R(im,in) = sum(P(s+1,in)*rand<=P(1:s,in));
s = s-R(im,in);
end
end
end
return
6 Comments
Yu Takahashi
on 9 Feb 2021
Edited: Walter Roberson
on 10 Feb 2021
Wondering whether it is possible to specify the max and min of the devided value? i.e., something like what you kindly provided in the randfixedsum function, thanks!
Ref
Bruno Luong
on 12 Aug 2023
@Walter Roberson "Wondering whether it is possible to specify the max and min of the devided value?"
More Answers (2)
Walter Roberson
on 2 Mar 2017
9 Comments
Walter Roberson
on 4 Mar 2017
Ah. I don't think I know how to implement your suggestion, though, at least not without generating all of the possible choices that sum to 20 and then picking one at random.
John D'Errico's https://www.mathworks.com/matlabcentral/fileexchange/12009-partitions-of-an-integer can calculate all of the possible partitions; a question is whether we can avoid having to take that step.
Walter Roberson
on 4 Mar 2017
https://en.wikipedia.org/wiki/Partition_(number_theory)#Restricted_part_size_or_number_of_parts talks about restricted partitioning briefly, and ties it to change making problems, which does indeed sound equivalent to the approach I was taking. Those are in turn tied to knapsack problems.
Bruno Luong
on 10 Aug 2020
m = 5;
n = 3;
s = 10;
This will generate uniform distribution with sum criteria
% generate non-negative integer random (m x n) array row-sum to s
[~,r] = maxk(rand(m,s+n-1),n-1,2);
z = zeros(m,1);
r = diff([z, sort(r,2), (s+n)+z],1,2)-1;
1 Comment
Bimal Ghimire
on 4 Oct 2020
While generating conditional random numbers, how can we generate random numbers that has a limit of some maximum value and have certain specified sum value?
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