# Is “underlying” the right word?

I am describing a mathematical model, where the probability density function of a variable is made up of two contributions, two distributions. Mathematically we would say that f(x) = g1(x) + g2(x).

Now: in the text I am writing something like this:

"the distribution f(x) is the sum of two underlying distributions, g1(x) and g2(x). [...] in order to estimate the parameters of the underlying distributions we use a parametric approach...."

I am trying to use "underlying" in the sense of "lying under".

What do you think? Is underlying the right word or should I address those distributions in a different way (how)?

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This is a perfectly legitimate use of the word, and I recall encountering it and using it myself in writing about statistics. It sounds fine to at least one native English speaker with a degree in mathematics.

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As a non-mathematician it made sense to me, too. I wonder, though, can operand be used as a modifier in this sort of situation? Would something like "operand distributions" make sense to a mathematician? – onomatomaniak Oct 15 '11 at 11:33
It's been a looong time, but I don't think I ever encountered that phrase. "Underlying distribution" is a fairly common idiom. – James McLeod Oct 15 '11 at 13:33
I think everybody would be confused by "operand distributions", but "component distributions" would work fine. – Peter Shor Oct 15 '11 at 15:55
I agree - I was just about to suggest "component distributions" when I saw this comment. In some ways, this is a better choice of words. – James McLeod Oct 15 '11 at 18:05
@Peter, James: surely component would strongly suggest that g1 and g2 are coming from orthogonal subspaces? It’s not quite clear to me if that’s the case in the OP’s situation. – PLL Oct 20 '11 at 18:20

I'd leave out 'underlying', 'in order', and some articles, and correct the mathematical terminology, because the sum of two probability distributions is not a probability distribution, but their average is. That is, I'd rephrase "the distribution f(x) is the sum of two underlying distributions, g1(x) and g2(x)... in order to estimate the parameters of the underlying distributions we use a parametric approach..." as "Distribution f(x) is the average of distributions g1(x) and g2(x)... to estimate the parameters of g1 and g2, we use a parametric approach...".