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 belowIn 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))
How should I create a single score with two values as input?
statistics
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_bThat 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