Maximum entropy copula with given diagonal section

被引：8

作者：

Butucea, Cristina ^{[1
]}

Delmas, Jean-Francois ^{[2
]}

Dutfoy, Anne ^{[3
]}

Fischer, Richard ^{[1
,2
,3
]}

机构：

[1] Univ Paris Est, Lab Anal & Math Appl, UMR 8050, UPEM,UPEC,CNRS, F-77454 Marne La Vallee, France

[2] Univ Paris Est, CERMICS ENPC, F-77455 Marne La Vallee, France

[3] EDF Res & Dev, Ind Risk Management Dept, F-92141 Clamart, France

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2015年 / 137卷

关键词：

Copula; Entropy; Diagonal section; ABSOLUTELY CONTINUOUS COPULAS; DISTRIBUTIONS; CONSTRUCTION; MINIMIZATION;

D O I：

10.1016/j.jmva.2015.01.003

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal section. We give an explicit criterion on the diagonal section for the existence of the optimal copula and give a closed formula for its entropy. We also provide examples for some diagonal sections of usual bivariate copulas and illustrate the differences between these copulas and the associated maximum entropy copula with the same diagonal section. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：61 / 81

页数：21

共 27 条

[11] Copulas with given diagonal sections: novel constructions and applications
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, 4040 Linz, Austria
不详
不详
不详
不详
[J]. Int. J. Uncertainty Fuzziness Knowledge Based Syst., 2007, 4 (397-410): : 397 - 410
[12] On the construction of families of absolutely continuous copulas with given restrictions
Erdely, A
González-Barrios, JM
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2006, 35 (04) : 649 - 659
[13] Fredricks GA, 1997, DISTRIBUTIONS WITH GIVEN MARGINALS AND MOMENT PROBLEMS, P129
[14] On copulas and their diagonals
Jaworski, Piotr
[J]. INFORMATION SCIENCES, 2009, 179 (17) : 2863 - 2871
[15] Joe H., 1997, MONOGRAPHS ON STATIS, V73
[16] Quasi-copulas with a given sub-diagonal section
Juan Quesada-Molina, Jose
Saminger-Platz, Susanne
Sempi, Carlo
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (12) : 4654 - 4673
[17] Minimally informative distributions with given rank correlation for use in uncertainty analysis
Meeuwissen, AMH
Bedford, T
[J]. JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 1997, 57 (1-4) : 143 - 174
[18] Nelsen R.B., 2006, SPRINGER SERIES IN S
[19] Best-possible bounds on sets of bivariate distribution functions
Nelsen, RB
Quesada-Molina, JJ
Rodríguez-Lallena, JA
Ubeda-Flores, M
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2004, 90 (02) : 348 - 358
[20] On the construction of copulas and quasi-copulas with given diagonal sections
Nelsena, Roger B.
Quesada-Molina, Jose Juan
Rodriguez-Lallena, Jose Antonio
Ubeda-Flores, Manuel
[J]. INSURANCE MATHEMATICS & ECONOMICS, 2008, 42 (02) : 473 - 483

← 1 2 3 →