On some descriptive aspects of measures of monotone dependence. (English) Zbl 0828.62050

Conti, Pier Luigi

Metron 51, No. 3-4, 43-60 (1993).

Summary: This paper is concerned with the construction of measures of monotone dependence. The approach is based on some principles substantially introduced by C. Gini in a not very formal way. Among them, the notion of “indifference”, as a synonym of “lack of concordance/discordance”, plays a basic role. After giving two different definitions of indifference (\(G\)-indifference and \(K\)-indifference), the author introduces measures of monotone dependence that agree with one of the above mentioned notions of indifference, and that work for general probability distribution functions. Finally, some other existing measures are discussed.

MSC:

62H20

Measures of association (correlation, canonical correlation, etc.)

Keywords:

\(G\)-indifference; construction of measures of monotone dependence; indifference; \(K\)-indifference