Quadratic-mean-of-order-r indexes of output, input and productivity

This paper deals with the quadratic-mean-of-order-r indexes of output, input and productivity. Each index is a family of indexes that unify many of the existing indexes, including the most popular ones. We show that all index number formulae belonging to these families are superlative indexes. This is considered as a generalization of the equivalence of Fisher and Malmquist indexes, shown by Diewert (1992).