Mahonian Z statistics

The ZZ statistic of Zeilberger and Bressoud is computed by summing the major index of the 2-letter subwords. We generalize this idea to other splittable Mahonian statistics. We call splittable Mahonian statistics which produce other splittable Mahonian statistics in this fashion ZZ-Mahonian  . We characterize ZZ-Mahonian statistics and include several examples.