Index express the similarity in shape between two data sets

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I have two data sets.One is points in the blue curve. The other is points in the green curve. Now I want to find a property (P) or something else like index that has the following characteristics:

1. It represents the similarity between two data sets.(With similarity I am referring to the same shapes plot by these points of two data sets)
2. It doesn't depend on the scale.Two shapes have the same shape but different scale still give the same P value.

Could you suggest what P should I consider?



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