Probability density function for binary data

I have data for the index of each point: 0 for the point outside particle, 1 for the points inside particle.

How to calculate calculate the PDF for this case? If you know that my domaine points is in [200 67].

And I want to calculate the PDF in a fixed x-point for example 80.

Answer 1

[Image Analyst]

Not sure what the PDF means in this context. You can compute the chance the particle will be a 0 or a 1. This would give a PDF with only two values on the x axis.

p(1) = sum(data == 0) / numel(data);
p(2) = sum(data == 1) / numel(data);

Is that what you want? Or do you have (x,y) locations for each point and want some sort of 2-D probability that the "1" will land at some location or radius?

[Tesla]

Thank you for the answer.

I mean by PDF the Probability density function.

Attached an example of my data. The data for the whole domain (67X335).

And I want a 2-D PDF that the "1" will land at some location, for me I am interested in a fixed x, for example in X=50. And See how the PDF is changing along Y axis.

The attached data is for 1 iterations, and I have around 1000 iterations. You can see the picture. This data is already done by Matlab.

So the PDF has to be the average for the whole data iterations.

[Image Analyst]

The workbook contains just one of those 67x335 matrices. The values are either -1, 0, or 1. Explain what the rows and columns represent.

[Tesla]

The workbook is just for 1 iteration, and its 67x335 matrices which meand 67 point in Y-axis and 335 point in X-axis.

When the values ares 1 means we are in inside the cell, and 0 means outside the cell. for -1 its means outside the domain of my calculations.

[Tesla]

Any clue?

[Image Analyst]

So the row number is y and the column index is x? So I can get the one's (x,y) coordinates by doing

[y, x] = find(theMatrix);

Correct? If so, why don't you just add the matrix at each iteration to a master, growing, cumulative matrix and then divide that matrix by the number of iterations to get the pdf?

[Tesla]

Yes correct. How can I do that?

[Image Analyst]

See the FAQ for how to read in different files

https://matlab.fandom.com/wiki/FAQ#How_can_I_process_a_sequence_of_files.3F

[Tesla]

Thank you,

But indeed my data are already stored on matlab variable, you can see the screenshot.

I am just worring how to use your suggestion to calculate the pdf.

[Image Analyst]

If ca is your cell array:

numCells = length(ca);
sumArray = zeros(67, 335);
for k = 1 : numCells
    thisCell = ca{k}; % A single 67x335 matrix.
    sumArray = sumArray + thisCell;
end
meanArray = sumArray / numCells;

Does that do what you want?

[Tesla]

The code is giving the total pdf for the whole domain. I want the pdf in a specified x-point.

For example in x=30. You see?

[Image Analyst]

Why isn't it just

% Get probability for various y values along the x=30 line.
pdf30 = meanArray(:, 30); 

[Tesla]

Thank you very much, it works!