How to find Joint PMF for three vectors using MATLAB

I want to find the joint Probability Mass Function of three vectors which are quite large in number; and I need to find joint PMF for three vectors. Following is the code written but I am getting error with it:

 % code

 clear all; clc

 filename = 'Case_I.xlsx';             
 num=xlsread('Case_I.xlsx');      %Case I Excel file contains data with 3 column vectors

 xi = linspace(min(num(:,1)), max(num(:,1)));
 yi = linspace(min(num(:,2)), max(num(:,2)));
 zi = linspace(min(num(:,3)), max(num(:,3)));

 hst = hist3(num,{xi yi zi});

 pmf = hst/sum(hst(:));

The error I am getting is:

Error using hist3 (line 119) Bin centers must be specified with a cell array containing two numeric vectors.

Error in CaseIV_JointPMF1 (line 9) hst = hist3(num,{xi yi zi});

Any help in this regard on finding the PMF of three or more vectors will be appreciated. Thanks.

Answer 1

[Hoda Akl]

Hello,

I just faced the same problem and I solved it the following way:

after you have your data in a matrix where the first column is variable 1, second is variable 2, third is variable 3 , which I assume is the matrix here that you call "num" ,

valuesx = sort(unique(num(:,1)));  %this gets the unique values of each variable 
valuesy = sort(unique(num(:,2)));
valuesz = sort(unique(num(:,3)));
probmat = zeros(length(valuesx),length(valuesy),length(valuesz));
for i=1:length(valuesx)
    for j=1:length(valuesy)
        for k = 1:length(valuesz)
            %the sum gets how many instances those three events occured
            %together and then divides by the total number of instances to
            %normalize the probability
            probmat(i,j,k) = (sum(num(:,1) == valuesx(i) & num(:,2) == valuesy(j) & num(:,3) == valuesz(k)))/size(num,1);
        end
    end
end
% probmat is your joint distribution

You should check that all values in probmat add up to 1.