Which of the Following Is an Archimedean Copula Over Two $F _ { 1 } , F _ { 2 }$

question 9

Multiple Choice

Which of the following is an Archimedean copula over two distribution functions $F _ { 1 } , F _ { 2 }$ ?

• A) \(C \left( F _ { 1 } , F _ { 2 } \right) = \ln \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { 1 / a } \right\}\)
• B) \(C \left( F _ { 1 } , F _ { 2 } \right) = \exp \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { a } \right\}\)
• C) \(C \left( F _ { 1 } , F _ { 2 } \right) = \exp \left\{ - \left[ \left( \ln \frac { 1 } { F _ { 1 } } \right) ^ { a } + \left( \ln \frac { 1 } { F _ { 2 } } \right) ^ { a } \right] ^ { 1 / a } \right\}\)
• D) None of the above.

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Definitions:

Cis-1,4-Dipropylcyclohexane

A cyclohexane derivative where two propyl groups are positioned on the same side of the cyclohexane ring at the 1st and 4th positions.

Stable Conformation

A molecular arrangement that is in a low energy state, making it less reactive and more resistant to changes.

Cis-1,2-Dimethylcyclohexane

An organic compound where two methyl groups are positioned on the same side of a cyclohexane ring, affecting its chemical and physical properties.

Stable Conformation

A molecular structure that is in a state of minimum energy and resists change.