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How to sum two probability density functions?

Asked by Jules Ray on 25 Feb 2019
Latest activity Commented on by John D'Errico
on 25 Feb 2019
I have created two probability density functions using this formula:
I would like to sum two of these pdfs and also substract both, but I have not idea how to do it.
Thanks in advance for your help
pd = fitdist(L1.Z(:),'Normal');
x_pdf = [min(L1.Z(:)):0.01:max(L1.Z(:))];
y = pdf(pd,x_pdf);


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2 Answers

Answer by ANKUR KUMAR on 25 Feb 2019
 Accepted Answer

"sum two of these pdfs and also substract both"?
Are you pretty sure to add the pdfs?
My suggestion is to first add data and then plot the pdf in the regular fashion.
If you facing some issues with plotting pdf, use join the tops of histograms of the data and convert y axis into percentage. This also gives you the probability of occurence of a number in your data.


Tnnks Ankur
Yes, I have been trying to perform operations with PDF's but seems to be simplest way perform these operation on the data and then calculate the PDF. I found a function (see link) that perfom sum between pdf's. The issue is when I compare results of both (working with the original data and by summing pdf's) both give different results and can only performed when matrix are equal size both. Just summing the data and applying pdf give a quite bell shaped curve, instead when suming both gives a bimodal curve. I dont know how to explain this.
you reply suggest "My suggestion is to first add data and then plot the pdf in the regular fashion", how would you add the data if the matrix are n*m and l*k both with different numbers of rows and cols?
There is no any compulsion of using the pre-defined pdf funciton in MATLAB.
PDF is nothing but the probability of occurence of each element.
Let's A is a matrix of m*n size. PDF of A is exactly same as the PDF of A(:).
So, if you wish to sum-up two data sets of different dimension, just convert into row matrices and then merge it up.
C=[A(:) ; B(:)];
DIrectly plot the PDF of matrix C. PDF just give the percentage of occurnce of element, nothing else.
One of the simplest way to plot Probability Distribution Function is use first draw histogram and then join their tops, follwed by converting Y axis into percentage.

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Answer by Jules Ray on 25 Feb 2019
Edited by Jules Ray on 25 Feb 2019

that was very clarifying
Just a quick question, this would be the example for add two pdf's: C=[A(:) ; B(:)];
what 's about substracting both?
Thanks again

  1 Comment

Please don't add answers just to ask another question.
Anyway, from reading your various comments, I don't think you understand what a PDF means. Forming the difference of two PDFs has almost no meaning that I can think of.
I think perhaps you want to form the sum and difference of two random variables? That is very, VERY different from forming the sum or difference of two PDFs. Perhaps that is what you mean.

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