| Title:
|
Bounds of general Fréchet classes (English) |
| Author:
|
Skřivánek, Jaroslav |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
130-143 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fréchet classes. Algebraic search for the bounds is interpreted as a solution to a linear system of Diophantine equations. Classical analytical specification of the bounds is described. (English) |
| Keyword:
|
copula |
| Keyword:
|
Fréchet class |
| Keyword:
|
Diophantine equation |
| MSC:
|
11D45 |
| MSC:
|
60E05 |
| MSC:
|
62H20 |
| idZBL:
|
Zbl 1251.60015 |
| idMR:
|
MR2932932 |
| . |
| Date available:
|
2012-03-05T08:35:15Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142067 |
| . |
| Reference:
|
[1] F. Durante, E. P. Klement, J. J. Quesada-Molina: Bounds for trivariate copulas with given bivariate marginals..J. Inequal. Appl. ID 161537 (2008). Zbl 1162.62047, MR 2481572 |
| Reference:
|
[2] P. Embrechts, F. Lindskog, A. McNeil: Modelling dependence with copulas and applications to risk management..In: Handbook of Heavy Tailed Distributions in Finance (S. T. Rachev, ed.), Elsevier/North-Holland 2003. |
| Reference:
|
[3] P. Embrechts: Copulas: A personal view..J. Risk Insurance 76 (2009), 3, 639-650. 10.1111/j.1539-6975.2009.01310.x |
| Reference:
|
[4] H. Joe: Multivariate models and Dependence Concepts..Chapman&Hall, London 1997. Zbl 0990.62517, MR 1462613 |
| Reference:
|
[5] R. B. Nelsen: Introduction to Copulas..Springer-Verlag, New York 2006. Zbl 1152.62030, MR 2197664 |
| Reference:
|
[6] C. Genest, J. Nešlehová: A primer on copulas for count data..Astin Bull. 37 (2007), 2, 475-515. MR 2422797, 10.2143/AST.37.2.2024077 |
| Reference:
|
[7] A. P. Tomás, M. Filgueiras: An algorithm for solving systems of linear Diophantine equations in naturals..In: Progress in Artificial Intelligence - EPIA'97, Lecture Notes in Artificial Intelligence 1323 (E. Costa and A. Cardoso, eds.), Springer-Verlag 1997, pp. 73-84. MR 1703009 |
| . |
