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I have two series of values, a and b as inputs and I want to create a score, c, which reflects both of them equally. The distribution of a and b are below

Distribution of a Distribution of b

In both cases, the x-axis is just an index.

How should I go about creating an equation c = f(a,b) such that a and b are (on average) represented equally in c?

Edit: c = (a+b)/2 or c = ab will not work because c will be too heavily weighted by a or b.

I need a function, f, where c = f(a,b) and c' = f(a + stdev(a),b) = f(a, b + stdev(b))

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2 Answers 2

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If you're looking for something where A and B are equally represented, consider trying something like Z score normalization (or standard score):

c = (a-u_a)/sigma_a + (b-u_b)/sigma_b

That score equally represents the two, but would be on a smaller scale. It really shouldn't matter since the numbers are arbitrary, however, if you need to scale it up, you could do something like:

c2 = (sigma_a+sigma_b)*(c) + u_a + u_b
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using R syntax:

 c <- a/2+b/2

or you can create a function:

c <- function(a,b) { return(a/2+b/2) }
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  • $\begingroup$ That's not going to help me. If I use an arithmetic mean, the score will be too heavily weighted by b in most cases. I need a change in each to equally be capable of influencing c. $\endgroup$ May 3, 2015 at 19:20

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