2D normal distribution fit

[Arman0712]

I want to perform a 2D normal fit to extraxt Correlation between X and Y. Somehow i  am not able to find any vi for the same. any help will be appreciated. I have an m*n array where row no. define x value and column define y value and Z is defined as (m,n) value

[altenbach]

Can you give an data example and a link to the theory you want to apply. What is the final output? A single scalar?

[altenbach]

Maybe something as discussed in this thread?

 

[Arman0712]

Not exactly this. I need to calculate the correlation between X and Y by bivariant fit..below attached is the theory and data(intensity graph).

 

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@altenbach wrote:

Maybe something as discussed in this thread?

 

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[altenbach]

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@Arman0712 wrote:

Not exactly this. I need to calculate the correlation between X and Y by bivariant fit..below attached is the theory and data(intensity graph). 

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Bivariate, not bivariant, right? Just plug the data into the formula, shouldn't be too hard....

You still have not attached any typical data.

[altenbach]

Your X and Y are just the array indices. It seems the advanced signal processing toolkit has some tools.

There are also some earlier discussions, so search the forum. (example)

[Arman0712]

Yess bivariate. her i am attaching the data

[altenbach]

The formulas you show in you picture are just for a symmetric 2D normal distribution (correlation=0) and a simplified version of my code (where there is only one global sigma) already does that. It won't be appropriate for your problem where you try to look at correlations, i.e. where the distribution has an elliptical cross-section that would be a circle for 0% correlation and collapse to a single line for 100% correlation.

You seem to be looking for this. All you probably need is use my 2D fit and look at the two axes of the ellipse. If they are equal there is no correlation and if one is zero, there is 100% correlation.

To just get the correlation coefficient, here's what you could also do. I am sure there are millions of other ways, but please verify.

[Arman0712]

If i change the correlation the distribution will change accordingly , i am attaching a picture generated in python for the same.

I cant use the the method you have shown as it will include all the outliners as well. i need to exclude those by normal ditribution fit. which will give me correlation between x and y.

[altenbach]

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@Arman0712 wrote:

I cant use the the method you have shown as it will include all the outliners as well. i need to exclude those by normal ditribution fit. which will give me correlation between x and y.

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Well, first you need to define what an "outlier" is.