Modelling Dependence with Copulas - IFOR

More documents

Recommendations

Info

4 Techniques for Construction of Multivariate <strong>Copulas</strong> and Ψ(v 2 ) − Ψ(v 1 ) v 2 − v 1 ≥ 1 u 2 + u 1 − 1 if u 1 + u 2 < 1. But inf{1/(u 1 + u 2 − 1)|0 ≤ u 1 ≤ u 2 ≤ 1,u 1 + u 2 > 1} =1and sup{1/(u 1 +u 2 −1)|0 ≤ u 1 ≤ u 2 ≤ 1,u 1 +u 2 < 1} = −1, and hence C is 2-increasing if and only if −1 ≤ Ψ(v 2) − Ψ(v 1 ) ≤ 1 v 2 − v 1 for v 1 ,v 2 in I such that v 1
4.2 The Marshall-Olkin Family As a consequence each parameter, θ, must satisfy |θ| < 1. Note that this is a proper multivariate extension since each k-margin, 3 ≤ k
Page 1: Eidgenössische Technische Hochschu
Page 5: Contents Contents 1 Motivation 1 2
Page 8 and 9: 1 Motivation distributions. Hence w
Page 10 and 11: 2 Copulas 1. DomC ′ = S 1 × S 2
Page 12 and 13: 2 Copulas Theorem 2.3. If C ′ is
Page 14 and 15: 2 Copulas Here C α1(X 1),α 2(X 2)
Page 16 and 17: 2 Copulas . • Simulate a value u
Page 18 and 19: 3 Dependence 3.2 Perfect Dependence
Page 20 and 21: 3 Dependence Thus ∫∫ P[(X 1 −
Page 22 and 23: 3 Dependence Proof. For both Kendal
Page 24 and 25: 3 Dependence Definition 11. Let X a
Page 26 and 27: 3 Dependence Furthermore if C is a
Page 30 and 31: 4 Techniques for Construction of Mu
Page 32 and 33: 4 Techniques for Construction of Mu
Page 35 and 36: 5 Archimedean Copulas In this chapt
Page 37 and 38: 5.2 Definitions (since ϕ and ϕ [
Page 39 and 40: 5.3 Properties 5.3 Properties For c
Page 41 and 42: 5.3 Properties Example 5.8. Conside
Page 43 and 44: 5.4 Order Theorem 5.7. Let ϕ be a
Page 45 and 46: 5.5 Multivariate Archimedean Copula
Page 47 and 48: 5.5 Multivariate Archimedean Copula
Page 49: 5.5 Multivariate Archimedean Copula
Page 52 and 53: 6 Elliptical Copulas Example 6.2. F
Page 54 and 55: 6 Elliptical Copulas We now address
Page 56 and 57: 6 Elliptical Copulas • • •
Page 59 and 60: 7 Extreme Value Copulas 7.1 Univari
Page 61 and 62: 7.2 Multivariate Extreme Value Theo
Page 63: 7.2 Multivariate Extreme Value Theo
Page 66 and 67: 8 Mixture of Extremal Distributions
Page 74 and 75: 9 Modelling Extremal Events in Prac
Page 76 and 77: 9 Modelling Extremal Events in Prac
Page 78 and 79:
9 Modelling Extremal Events in Prac
Page 80 and 81:
Page 82 and 83:
Page 85:
10 Conclusions In this paper we hav
Page 88 and 89:
11 Appendix { if(rcor[row,col] == 1
Page 90 and 91:
11 Appendix lognormal
Page 93:
References References [1] Dhaene J.
show all

Modelling Dependence with Copulas - IFOR

Create successful ePaper yourself

Delete template?

Save as template?