Nothing says you can’t take the geometric mean of a series that includes negative numbers, just that if you have an even number of elements, but an odd number of negative elements, you’ll get a complex answer.
To weight the elements of your series, you should be able to take the geometric mean of p(X)*X, then divide by the geometric mean of your p(X).
Edit: said something very silly about weighting.
Nothing says you can’t take the geometric mean of a series that includes negative numbers, just that if you have an even number of elements, but an odd number of negative elements, you’ll get a complex answer.
To weight the elements of your series, you should be able to take the geometric mean of p(X)*X, then divide by the geometric mean of your p(X).