Others came along in the 1920s such as Irving Fisher and Correa MoylanWalsh to further build on Lowe, Laspeyres, Paasche, and others to form more advanced models. The difference between older and newer indices is the older indexes fix weight using an arithmetic mean while the newer indices use a chain link or fix weight with a geometric mean.
The Hermann Paasche Index in a longer form:
The Fisher Quantity Index is a chain link of the Fisher Ideal index and identified by this formula:
This formula is employed by governments ...