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...".
Update (Response to 2 comments)
I see use of 'underlying' as pompously verbose, and also somewhat misleading. While one could say, for example, "7 is the sum of the underlying numbers 2 and 5," it is far more direct to say "7 equals 2 plus 5." The word 'underlying' contributes nothing to this simple example, and contributes relatively little to the question's example.
Given the further information that the sum is a weighted sum of multiple distributions, I have less objection to use of 'underlying', although still see it as verbose, and for the second instance of it might substitute 'basis' if appropriate. For example: "Distribution f(x) is a weighted sum of distributions g_1(x) ... g_k(x)... we use a parametric approach to characterize the g_i basis functions...".