Toward a language for specifying summarizing statistics

We introduce the ordered weighted averaging (OWA) operator and discuss how it can provide a basis for generating summarizing statistics over large data sets. We further note how different forms of OWA operators can be induced using weight generating functions. We show how these weight generating functions can provide a vehicle with which a data analyst can express desired summarizing statistics. Our goal here, is to develop an understanding of the relationship between weight generating functions and resulting summarizing statistics.