How to extract a PDF from points with a weigh attached to them

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Bert Taekels 2017-10-18

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https://ww2.mathworks.cn/matlabcentral/answers/361899-how-to-extract-a-pdf-from-points-with-a-weigh-attached-to-them

编辑： Peter Cook 2017-10-18

I Have a n by 3 matrix (lets say n = 100) where the 2 first collums are the x and y position of the point. The third collum is the weight of the particle (that got updated in a previous command). Now I would like to extract a bivariate norm pdf from these weighted points. I have found the fitgmdist command, but this does not include the weight of the points. Is there a way to do this. I have to say i'm still quite new in the matlab software Thanks

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Answer 1

Peter Cook 2017-10-18

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https://ww2.mathworks.cn/matlabcentral/answers/361899-how-to-extract-a-pdf-from-points-with-a-weigh-attached-to-them#answer_286485

编辑：Peter Cook 2017-10-18

I don't know if there's a canned function for this - you could try:

1. Compute weighted mean for each column of X

2. Compute covariance matrix using weighted mean (or skip #1 and compute a weighted covariance matrix directly - I am not sure if this produces the exact same result)

3. Compute eigenvalues & eigenvectors of covariance matrix

4. Use the eigenvectors corresponding to 2 largest eigenvalues to extract coefficients for the bivariate normal distribution