A few generalizations of Kendall's tau. Part II: Intrinsic meaning, properties, and computational aspects

被引：0

作者：

Manstavicius, Martynas ^{[1
]}

机构：

[1] Vilnius Univ, Inst Math, Fac Math & Informat, Naugarduko Str 24, LT-03225 Vilnius, Lithuania

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2025年 / 30卷 / 02期

关键词：

Kendall's tau; Scarsini axioms; bivariate copula; transformation; concordance measure; convex capacity; supermodular; MULTIVARIATE MEASURES; CONCORDANCE;

D O I：

10.15388/namc.2025.30.38964

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Continuing our investigation on generalizations of Kendall's tau, started in Part I of the paper, here we elaborate on the intrinsic meaning and degree of such polynomial-type concordance measures, as well as present many examples of their computation. In particular, we interpret generalized Kendall's tau phi as the difference between the average capacities of concordance and discordance, and, for power-type distortion functions phi, we obtain polynomial-type concordance measures of various degree, which could stimulate further research of their characterization as achieved for degree-one polynomial-type concordance measures by Taylor, Edwards, and Mikusin<acute accent>ski.

引用

页码：231 / 251

页数：21