- *Student's-t Copulas*

The parameter of dependence structure *Rt* and the degree of freedom *υ* can be estimated by maximum likelihood:

$$(\hat{R}\_l; \boldsymbol{\vartheta}) = \underset{(R\_l; \boldsymbol{\nu})}{\text{argmax}} \sum\_{i=1}^n \log c\_l(\hat{x}\_i; R\_l; \boldsymbol{\nu}) \tag{10}$$

In which, *ct*(*x*-, *Rt*; *υ*) denotes the density function of the Student's-t Copulas with parameter (*Rt*; *<sup>υ</sup>*). This refers to the study of Kotz and Nadarajah (2004).
