Geometric mean is nth root of product of n numbers.

If you replace any of those numbers with 0, it will all collapse to 0 - perhaps not what you want. But it's not hard to write such a program:

      geometric_mean1 =: (+/ % #) &. (^."1) @: (0&>.)
      geometric_mean1 2 4 8
   4
      geometric_mean1 _2 4 8
   0

If you want to replace negative numbers with their positive counterparts, you may first replace a number with its absolute value:

      geometric_mean2 =: (+/ % #) &. (^."1) @: (>. -)
      geometric_mean2 _2 4 8
   4
      geometric_mean2 2 4 8
   4

Original geometric_mean probably meant to be

      geometric_mean =: (+/ % #) &. (^."1)

- note the copula (assignment symbol) and rank of first verb (^.) .