| Title |
Bounds for the Clayton copula |
| Authors |
Manstavičius, Martynas ; Leipus, Remigijus |
| DOI |
10.15388/NA.2017.2.7 |
| Full Text |
|
| Is Part of |
Nonlinear analysis : modelling and control.. Vilnius : Vilnius University Institute of Mathematics and Informatics. 2017, Vol. 22, no 2, p. 248-260.. ISSN 1392-5113 |
| Keywords [eng] |
Archimedean copula ; Clayton copula ; copula bounds ; negative dependence |
| Abstract [eng] |
We provide two upper bounds on the Clayton copula C θ (u 1 ,...,u n ) if θ > 0 and n > 2 and a lower bound in the case θ ∈ [−1,0) and n > 2. The obtained bounds provide a nice probabilistic interpretation related to some negative dependence structures and also allow defining three new two-dimensional copulas, which tighten the classical Fréchet–Hoeffding bounds for the Clayton copula when n = 2. |
| Published |
Vilnius : Vilnius University Institute of Mathematics and Informatics |
| Type |
Journal article |
| Language |
English |
| Publication date |
2017 |
| CC license |
|
