# How can I determine the similarity of these graphs/curves?

I have 3 visually similar graphs pictured below. They have similar peak patterns that are visible to the naked eye, but I want to compare their similarity mathematically.

I can sum each column to flatten the intensity present, giving you a line curve so the intensity need not be a factor necessarily.

I'm not sure what domain/strategy I should be looking at. I want to essentially measure the similarity of the curves, but since amplitude can vary to some extent, I'm not sure how that would be accounted for, and I'm frankly a bit out of my depths here and don't know exactly where to look.

Any help in direction would be most appreciated.

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Noisy data? Interesting... Any suspected distribution? Could use some statistic test to check against it (or just against one of them assuming it is 100% correct)... – vonbrand Feb 5 '13 at 2:13
I don't think I'd actually call this off topic here, but it wouldn't surprise me if you'd get better results asking it at stats.stackexchange.com. – Micah Feb 5 '13 at 2:48
whats the graph of their differences look like? What is the way to measure how some function approximates another function? – Arjang Feb 5 '13 at 3:16

Let's suppose we want to compare two functions $p(t)$ and $q(t)$. I'm assuming that these two functions are defined over the same range of values, so it makes sense to compare $p(t)$ with $q(t)$ for all values of $t$. Suppose you know the function values at $n$ points, $t_1,t_2, \dots, t_n$.
Spaces of functions have many different "metrics" (ways of measuring the distance between functions). For your purpose, a reasonable one might be the $\ell_2$ metric. This says that $$distance(p,q) = \sqrt{ \sum_{i=1}^n (p(t_i) - q(t_i))^2 }$$