Table 1 Parameters of the fitted univariate distributions. Note that due to symmetry, we would expect a mean (i.e., location) of 0 for the distributions of A and \(Z_2 - Z_1\), which is in fact (almost) the case for the fitted values.

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

 

Distribution

Sample

Parameters

Location

Scale

Mean

Var

\(A~[\text {rad}]\)

Gen. normal

1

0.81

0

0.09

0

0.04

  

2

0.68

0

0.04

0

0.02

\(Z_1~[\text {mm}]\)

Gen. normal

1

14.71

1.20

0.98

1.20

0.31

  

2

4.38

1.69

1.14

1.69

0.43

\(Z_2-Z_1\)

Gen. normal

1

1.69

0

0.02

0

0

\({[}\text {mm}]\)

 

2

3.12

0

0.03

0

0

  1. The distribution of \(Z_1\) essentially dictates the extent of the structures in z-direction, where the mean values corresponds to roughly half the thickness of the samples. Note that B adheres to the same distribution as A, and \(Z_3 - Z_2\) has the same distribution as \(Z_2 - Z_1\). The units given in the left columns apply also to the location and scale parameters.
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