Polynomial bivariate copulas of degree five: characterization and some particular inequalities

Author:

Šeliga Adam1ORCID,Kauers Manuel2ORCID,Saminger-Platz Susanne3ORCID,Mesiar Radko1ORCID,Kolesárová Anna4ORCID,Klement Erich Peter3ORCID

Affiliation:

1. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering , Slovak University of Technology , Bratislava , Slovakia

2. Institute for Algebra , Johannes Kepler University , Linz , Austria

3. Department of Knowledge-Based Mathematical Systems , Johannes Kepler University , Linz , Austria

4. Institute of Information Engineering, Automation and Mathematics , Faculty of Chemical and Food Technology , Slovak University of Technology , Bratislava , Slovakia

Abstract

Abstract Bivariate polynomial copulas of degree 5 (containing the family of Eyraud-Farlie-Gumbel-Morgenstern copulas) are in a one-to-one correspondence to certain real parameter triplets (a, b, c), i.e., to some set of polynomials in two variables of degree 1: p(x, y) = ax + by + c. The set of the parameters yielding a copula is characterized and visualized in detail. Polynomial copulas of degree 5 satisfying particular (in)equalities (symmetry, Schur concavity, positive and negative quadrant dependence, ultramodularity) are discussed and characterized. Then it is shown that for polynomial copulas of degree 5 the values of several dependence parameters (including Spearman’s rho, Kendall’s tau, Blomqvist’s beta, and Gini’s gamma) lie in exactly the same intervals as for the Eyraud-Farlie-Gumbel-Morgenstern copulas. Finally we prove that these dependence parameters attain all possible values in ]−1, 1[ if polynomial copulas of arbitrary degree are considered.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Modeling and Simulation,Statistics and Probability

Reference100 articles.

1. [1] Abel, N. H. (1826). Untersuchung der Functionen zweier unabhängig veränderlichen Größen x und y, wie f (x, y), welche die Eigenschaft haben, daß f (z, f (x, y)) eine symmetrische Function von z, x und y ist. J. Reine Angew. Math. 1, 11–15.

2. [2] Alsina, C., M. J. Frank, and B. Schweizer (2006). Associative Functions. World Scientific Publishing, Singapore.

3. [3] Amblard, C. and S. Girard (2009). A new extension of bivariate FGM copulas. Metrika 70, 1–17.

4. [4] Anakkamatee, W., S. Dhompongsa, and S. Tasena (2014). A constructive proof of the Sklar’s theorem on copulas. J. Nonlinear Convex Anal. 15(6), 1137–1145.

5. [5] Barlow, R. E. and F. Proschan (1981). Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring MD.

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3