Question

I have a problem in my MATLAB code. Let me first give you some explanation about the issue. I have two matrices which represent probabilities of specific outcomes of events. The first one is called DemandProbabilityMatrix or in short DemandP. Entry (i,j) shows the probability that item i is demanded j many times. Similarly, we have a ReturnProbabilityMatrix, i.e. ReturnP. An element of type (i,j) stores the probability that item i is returned j many times.
We want to compute the net demand probability out of these two matrices. For an example:

DemandP=[ .4 .5 .1]
ReturnP=[ .2 .3 .5]

In this case we have 1 item and it can be demanded or returned either 1,2 or 3 times with the given probabilities. To be more specific That item will be demanded just for once with probability .4 .

Then we need to compute the net demand. In this case, net demand can be -2,-1,0,1 or 2. For instance in order to get a net demand of -1 we can either have a demand of 1 and return of 2 or demand of 2 and return of 3. Thus we have

NetDemandP(1,2)= DemandP(1,1)*ReturnP(1,2)+DemandP(1,2)*ReturnP(1,3).

Thus the NetDemandP should look as:

NetDemandP=[.20 .37 .28 .13 .02]

I can do this with nested for loops but I’m trying to come up with a faster way. In case it helps I have the following for loops solutions where I denotes the number of rows in ReturnP and DemandP, J+1 denotes the number of columns in those matrices.

NetDemandP=zeros(I,2*J+1);
    for i=1:I
        for j=1:J+1
            for k=1:J+1
                NetDemandP(i,j-k+J+1)=NetDemandP(i,j-k+J+1)+DemandP(i,j)*ReturnP(i,k);
            end
        end
    end

Thanks in advance

Answer 1

What you want is the convolution of your probability density functions. Or, more specifically, you want the convolution of the demand density with the reverse of the return density. This is easily achieved in Matlab. For example:

DemandP = [.4 .5 .1];
ReturnP = [.2 .3 .5];
NetDemandP = conv(DemandP,fliplr(ReturnP))

If you have matrices instead of vectors, then just iterate through the rows:

for i = 1:size(DemandP,1)
    NetDemandP(i,:) = conv(DemandP(i,:),fliplr(ReturnP(i,:)))
end