Means and their applications. (English) Zbl 1043.91015

Ostasiewicz, Stanisława; Ostasiewicz, Walenty

Ann. Oper. Res. 97, 337-355 (2000).

Summary: General considerations about means and expectations are preceded by a short historical overview. The existing approaches to the definition of means are classified into three groups: approximational, functional, and axiomatic. In some particular cases all of them are equivalent. The problem of meaningfulness of means is discussed for ordinal data and for some important cases of metric data. A survey of the main areas of applications: decision theory, group decision, insurance, economical equity and inequality is also provided.

MSC:

62A01

Foundations and philosophical topics in statistics

Keywords:

mean; average; expectation; meaningfulness; poverty; inequality