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I am not really sure how to describe it with the correct mathematical terms. If there are any questions, I will try to explain further.

I have several instances of a group of proportions. One could say I have several pie charts, where each pie chart has the same kind of pieces (classes) and the pie's pieces always sum to one. Examples: Pie 1 Pie 2

I am searching for a method for comparing these distributions. I have thought of a method but am not sure if that is scientific, it may already exist and have a proper name.

The method compares the different slices/classes of the distributions that I want to compare. The minimum value of the shares is computed and summed up. The result of this is always in the interval of 0 to 1, with 1 being identical distributions and 0 being completely different distributions.

For comparing the examples the result of this similarity measure would be 0.75 In pseudocode: (min(pie1_class1, pie2_class1) + min(pie1_class2, pie2_class2) + min(pie1_class3, pie2_class3))

Is there a name for such a similarity measure? Is there a more appropriate similarity measure?

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This is one minus the Bray-Curtis dissimilarity between two compositions expressed as proportions.

See: https://en.wikipedia.org/wiki/Bray%E2%80%93Curtis_dissimilarity

This is a widely used measure in ecology. There are other ways to measure the similarity or dissimilarity between compositions but I don't know much about them.

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  • $\begingroup$ that's it, Thanks a lot, $\endgroup$
    – Georg Schneeberger
    Commented Mar 12, 2023 at 10:37

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