Table 2 Parameters of the fitted copulas.

From: Copula-based modeling and simulation of 3D systems of curved fibers by isolating intrinsic fiber properties and external effects

 

Copula

Sample

Parameters

Rotation

(A, B)

Student’s t

1

(0.66, 3.15)

0

2

(0.82, 3.11)

0

\((Z_3 - Z_2, Z_1)\)

Clayton

1

0.05

90

2

0.06

90

\((Z_2 - Z_1, Z_1)\)

Clayton

1

0.02

90

2

0.03

90

\((Z_3 - Z_2, Z_2 - Z_1) | Z_1\)

Student’s t

1

(0.93, 2.05)

0

2

(0.99, 5.00)

0

  1. The results stated in the last three rows are used to build a trivariate R-vine copula for \((Z_1, Z_2-Z_1, Z_3-Z_2)\). Parameters for Student’s t-copulas are given as \((\rho , \nu )\).
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